Root subsystems of B^{1}

so(15), type $B^{1}_7$
Structure constants and notation.
Root subalgebras / root subsystems.
sl(2)-subalgebras.

Page generated by the calculator project.

g: B^{1}_7. There are 110 table entries (= 108 larger than the Cartan subalgebra + the Cartan subalgebra + the full subalgebra).

Type k_{ss}: B^{1}_7 (Full subalgebra) Type C(k_{ss})_{ss}: 0	Type k_{ss}: D^{1}_7 Type C(k_{ss})_{ss}: 0	Type k_{ss}: D^{1}_6+A^{2}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_5+2A^{1}_1 Type C(k_{ss})_{ss}: 0
Type k_{ss}: D^{1}_5+B^{1}_2 Type C(k_{ss})_{ss}: 0	Type k_{ss}: D^{1}_5+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_4+A^{1}_3 Type C(k_{ss})_{ss}: 0	Type k_{ss}: D^{1}_4+B^{1}_3 Type C(k_{ss})_{ss}: 0
Type k_{ss}: D^{1}_4+A^{1}_3 Type C(k_{ss})_{ss}: 0	Type k_{ss}: D^{1}_4+A^{2}_1+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_3+4A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: 2A^{1}_3+A^{2}_1 Type C(k_{ss})_{ss}: 0
Type k_{ss}: A^{1}_3+B^{1}_2+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_3+4A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{2}_1+6A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_6 Type C(k_{ss})_{ss}: 0
Type k_{ss}: D^{1}_6 Type C(k_{ss})_{ss}: A^{2}_1	Type k_{ss}: A^{1}_6 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_5+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: D^{1}_5+A^{2}_1 Type C(k_{ss})_{ss}: 0
Type k_{ss}: D^{1}_5+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: A^{1}_5+A^{2}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_4+A^{1}_2 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_4+2A^{1}_1 Type C(k_{ss})_{ss}: 0
Type k_{ss}: D^{1}_4+B^{1}_2 Type C(k_{ss})_{ss}: 0	Type k_{ss}: D^{1}_4+A^{1}_2 Type C(k_{ss})_{ss}: 0	Type k_{ss}: D^{1}_4+A^{2}_1+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: D^{1}_4+2A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1
Type k_{ss}: A^{1}_4+B^{1}_2 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_4+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_3+A^{1}_3 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_3+A^{1}_3 Type C(k_{ss})_{ss}: 0
Type k_{ss}: B^{1}_3+3A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: 2A^{1}_3 Type C(k_{ss})_{ss}: A^{2}_1	Type k_{ss}: 2A^{1}_3 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_3+B^{1}_2+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1
Type k_{ss}: A^{1}_3+A^{1}_2+A^{2}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_3+A^{2}_1+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_3+A^{2}_1+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_3+3A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1
Type k_{ss}: B^{1}_2+A^{1}_2+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_2+4A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_2+4A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{2}_1+5A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1
Type k_{ss}: 6A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1	Type k_{ss}: B^{1}_5 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: D^{1}_5 Type C(k_{ss})_{ss}: B^{1}_2	Type k_{ss}: A^{1}_5 Type C(k_{ss})_{ss}: A^{2}_1
Type k_{ss}: B^{1}_4+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: D^{1}_4+A^{2}_1 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: D^{1}_4+A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1+A^{1}_1	Type k_{ss}: A^{1}_4+A^{2}_1 Type C(k_{ss})_{ss}: 0
Type k_{ss}: A^{1}_4+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: B^{1}_3+A^{1}_2 Type C(k_{ss})_{ss}: 0	Type k_{ss}: B^{1}_3+2A^{1}_1 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: B^{1}_3+2A^{1}_1 Type C(k_{ss})_{ss}: 2A^{1}_1
Type k_{ss}: A^{1}_3+B^{1}_2 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: A^{1}_3+B^{1}_2 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_3+A^{1}_2 Type C(k_{ss})_{ss}: A^{2}_1	Type k_{ss}: A^{1}_3+A^{1}_2 Type C(k_{ss})_{ss}: 0
Type k_{ss}: A^{1}_3+A^{2}_1+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: A^{1}_3+A^{2}_1+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: A^{1}_3+2A^{1}_1 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: A^{1}_3+2A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1
Type k_{ss}: A^{1}_3+2A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_2	Type k_{ss}: B^{1}_2+A^{1}_2+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: B^{1}_2+3A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: 2A^{1}_2+A^{2}_1 Type C(k_{ss})_{ss}: 0
Type k_{ss}: A^{1}_2+A^{2}_1+2A^{1}_1 Type C(k_{ss})_{ss}: 0	Type k_{ss}: A^{1}_2+3A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: A^{2}_1+4A^{1}_1 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: A^{2}_1+4A^{1}_1 Type C(k_{ss})_{ss}: 2A^{1}_1
Type k_{ss}: 5A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1+A^{1}_1	Type k_{ss}: B^{1}_4 Type C(k_{ss})_{ss}: A^{1}_3	Type k_{ss}: D^{1}_4 Type C(k_{ss})_{ss}: B^{1}_3	Type k_{ss}: A^{1}_4 Type C(k_{ss})_{ss}: B^{1}_2
Type k_{ss}: B^{1}_3+A^{1}_1 Type C(k_{ss})_{ss}: 3A^{1}_1	Type k_{ss}: A^{1}_3+A^{2}_1 Type C(k_{ss})_{ss}: A^{1}_3	Type k_{ss}: A^{1}_3+A^{2}_1 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: A^{1}_3+A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_2+A^{1}_1
Type k_{ss}: A^{1}_3+A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1+A^{1}_1	Type k_{ss}: B^{1}_2+A^{1}_2 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: B^{1}_2+2A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_3	Type k_{ss}: B^{1}_2+2A^{1}_1 Type C(k_{ss})_{ss}: 2A^{1}_1
Type k_{ss}: 2A^{1}_2 Type C(k_{ss})_{ss}: A^{2}_1	Type k_{ss}: A^{1}_2+A^{2}_1+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_1	Type k_{ss}: A^{1}_2+2A^{1}_1 Type C(k_{ss})_{ss}: 2A^{1}_1	Type k_{ss}: A^{1}_2+2A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_2
Type k_{ss}: A^{2}_1+3A^{1}_1 Type C(k_{ss})_{ss}: 3A^{1}_1	Type k_{ss}: A^{2}_1+3A^{1}_1 Type C(k_{ss})_{ss}: 3A^{1}_1	Type k_{ss}: 4A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_3	Type k_{ss}: 4A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1+2A^{1}_1
Type k_{ss}: B^{1}_3 Type C(k_{ss})_{ss}: D^{1}_4	Type k_{ss}: A^{1}_3 Type C(k_{ss})_{ss}: B^{1}_3	Type k_{ss}: A^{1}_3 Type C(k_{ss})_{ss}: B^{1}_4	Type k_{ss}: B^{1}_2+A^{1}_1 Type C(k_{ss})_{ss}: A^{1}_3+A^{1}_1
Type k_{ss}: A^{1}_2+A^{2}_1 Type C(k_{ss})_{ss}: A^{1}_3	Type k_{ss}: A^{1}_2+A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_2+A^{1}_1	Type k_{ss}: A^{2}_1+2A^{1}_1 Type C(k_{ss})_{ss}: D^{1}_4	Type k_{ss}: A^{2}_1+2A^{1}_1 Type C(k_{ss})_{ss}: 4A^{1}_1
Type k_{ss}: 3A^{1}_1 Type C(k_{ss})_{ss}: A^{2}_1+3A^{1}_1	Type k_{ss}: 3A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_3+A^{1}_1	Type k_{ss}: B^{1}_2 Type C(k_{ss})_{ss}: D^{1}_5	Type k_{ss}: A^{1}_2 Type C(k_{ss})_{ss}: B^{1}_4
Type k_{ss}: A^{2}_1+A^{1}_1 Type C(k_{ss})_{ss}: D^{1}_4+A^{1}_1	Type k_{ss}: 2A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_3+2A^{1}_1	Type k_{ss}: 2A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_5	Type k_{ss}: A^{2}_1 Type C(k_{ss})_{ss}: D^{1}_6
Type k_{ss}: A^{1}_1 Type C(k_{ss})_{ss}: B^{1}_5+A^{1}_1	Type k_{ss}: 0 (Cartan subalgebra) Type C(k_{ss})_{ss}: B^{1}_7

There are 45 parabolic, 45 pseudo-parabolic but not parabolic and 20 non pseudo-parabolic root subsystems.

The roots needed to generate the root subsystems are listed below.
["parabolic","0", []],
["parabolic","A^{1}_1", [[1, 2, 2, 2, 2, 2, 2]]],
["parabolic","A^{2}_1", [[1, 1, 1, 1, 1, 1, 1]]],
["parabolic","2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, 0, 1, 2, 2, 2, 2]]],
["parabolic","A^{2}_1+A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2]]],
["parabolic","A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0]]],
["parabolic","B^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1]]],
["parabolic","3A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, 0, 1, 2, 2, 2, 2], [0, 0, 0, 0, 1, 2, 2]]],
["parabolic","A^{2}_1+2A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 0, 0, 1, 2, 2, 2]]],
["parabolic","A^{1}_2+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2]]],
["parabolic","A^{1}_2+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1]]],
["parabolic","B^{1}_2+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2]]],
["parabolic","A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0]]],
["parabolic","B^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1]]],
["parabolic","A^{2}_1+3A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, 0, 1, 2]]],
["parabolic","A^{1}_2+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, 0, 1, 2]]],
["parabolic","A^{1}_2+A^{2}_1+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 1, 2, 2]]],
["parabolic","2A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0]]],
["parabolic","B^{1}_2+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2], [0, 0, 0, 0, 1, 2, 2]]],
["parabolic","B^{1}_2+A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2], [0, 0, 0, -1, 0, 0, 0]]],
["parabolic","A^{1}_3+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2]]],
["parabolic","A^{1}_3+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1]]],
["parabolic","B^{1}_3+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2]]],
["parabolic","A^{1}_4", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0]]],
["parabolic","B^{1}_4", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, -1, -1, -1]]],
["parabolic","2A^{1}_2+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1]]],
["parabolic","B^{1}_2+A^{1}_2+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2]]],
["parabolic","A^{1}_3+A^{2}_1+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 2]]],
["parabolic","A^{1}_3+A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, 0]]],
["parabolic","A^{1}_3+B^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, -1]]],
["parabolic","B^{1}_3+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, 0, 1, 2]]],
["parabolic","B^{1}_3+A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0]]],
["parabolic","A^{1}_4+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2]]],
["parabolic","A^{1}_4+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 1]]],
["parabolic","B^{1}_4+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, -1, -1, -1], [0, 0, 0, 0, 1, 2, 2]]],
["parabolic","A^{1}_5", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0]]],
["parabolic","B^{1}_5", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, -1, -1]]],
["parabolic","B^{1}_3+A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0]]],
["parabolic","A^{1}_4+B^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, -1]]],
["parabolic","B^{1}_4+A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, -1, -1, -1], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, 0]]],
["parabolic","A^{1}_5+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1]]],
["parabolic","B^{1}_5+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, -1, -1], [0, 0, 0, 0, 0, 1, 2]]],
["parabolic","A^{1}_6", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0]]],
["parabolic","B^{1}_6", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1, -1]]],
["parabolic","B^{1}_7", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, -1]]],
["pseudoParabolicNonParabolic","2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [1, 0, 0, 0, 0, 0, 0]]],
["pseudoParabolicNonParabolic","3A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 2, 2, 2]]],
["pseudoParabolicNonParabolic","A^{2}_1+2A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 1, 0, 0, 0, 0, 0]]],
["pseudoParabolicNonParabolic","A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0]]],
["pseudoParabolicNonParabolic","4A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 2, 2, 2], [0, 0, 0, 0, 1, 2, 2]]],
["pseudoParabolicNonParabolic","A^{2}_1+3A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2]]],
["pseudoParabolicNonParabolic","A^{1}_2+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0]]],
["pseudoParabolicNonParabolic","B^{1}_2+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2], [0, 0, 1, 0, 0, 0, 0]]],
["pseudoParabolicNonParabolic","A^{1}_3+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2]]],
["pseudoParabolicNonParabolic","A^{1}_3+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1]]],
["pseudoParabolicNonParabolic","D^{1}_4", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2]]],
["pseudoParabolicNonParabolic","A^{2}_1+4A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, 0, 1, 2]]],
["pseudoParabolicNonParabolic","A^{1}_2+3A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2]]],
["pseudoParabolicNonParabolic","A^{1}_2+A^{2}_1+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 0, 0]]],
["pseudoParabolicNonParabolic","B^{1}_2+3A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2]]],
["pseudoParabolicNonParabolic","A^{1}_3+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 0, 0]]],
["pseudoParabolicNonParabolic","A^{1}_3+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, 0, 1, 2]]],
["pseudoParabolicNonParabolic","A^{1}_3+A^{2}_1+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 1, 2, 2]]],
["pseudoParabolicNonParabolic","A^{1}_3+A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0]]],
["pseudoParabolicNonParabolic","A^{1}_3+B^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, -1, -1]]],
["pseudoParabolicNonParabolic","B^{1}_3+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0]]],
["pseudoParabolicNonParabolic","D^{1}_4+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 2, 2]]],
["pseudoParabolicNonParabolic","D^{1}_4+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 1, 1]]],
["pseudoParabolicNonParabolic","D^{1}_5", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, -2, -2, -2]]],
["pseudoParabolicNonParabolic","B^{1}_2+A^{1}_2+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["pseudoParabolicNonParabolic","A^{1}_3+A^{2}_1+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["pseudoParabolicNonParabolic","A^{1}_3+A^{1}_2+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, 0, 1]]],
["pseudoParabolicNonParabolic","A^{1}_3+B^{1}_2+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, -1, -1], [0, 0, 0, 0, 0, 1, 2]]],
["pseudoParabolicNonParabolic","2A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, -1, 0, 0]]],
["pseudoParabolicNonParabolic","B^{1}_3+3A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2]]],
["pseudoParabolicNonParabolic","B^{1}_3+A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 0]]],
["pseudoParabolicNonParabolic","A^{1}_4+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["pseudoParabolicNonParabolic","D^{1}_4+A^{2}_1+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 2]]],
["pseudoParabolicNonParabolic","D^{1}_4+A^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, 0]]],
["pseudoParabolicNonParabolic","D^{1}_4+B^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, -1]]],
["pseudoParabolicNonParabolic","B^{1}_4+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, -1, -1, -1], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 0, 0]]],
["pseudoParabolicNonParabolic","D^{1}_5+A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, -2, -2, -2], [0, 0, 0, 0, 0, 1, 2]]],
["pseudoParabolicNonParabolic","D^{1}_5+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, -2, -2, -2], [0, 0, 0, 0, 0, 1, 1]]],
["pseudoParabolicNonParabolic","D^{1}_6", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, -1, -2, -2]]],
["pseudoParabolicNonParabolic","D^{1}_4+B^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, 0, -1]]],
["pseudoParabolicNonParabolic","B^{1}_4+A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, -1, -1, -1], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, -1, 0, 0]]],
["pseudoParabolicNonParabolic","D^{1}_5+B^{1}_2", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, -2, -2, -2], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 0, -1]]],
["pseudoParabolicNonParabolic","B^{1}_5+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, -1, -1], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["pseudoParabolicNonParabolic","D^{1}_6+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, -1, -2, -2], [0, 0, 0, 0, 0, 0, 1]]],
["pseudoParabolicNonParabolic","D^{1}_7", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1, -2]]],
["nonPseudoParabolic","4A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 2, 2, 2], [0, 0, 1, 0, 0, 0, 0]]],
["nonPseudoParabolic","5A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 2, 2, 2], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2]]],
["nonPseudoParabolic","A^{2}_1+4A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0]]],
["nonPseudoParabolic","A^{1}_3+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0]]],
["nonPseudoParabolic","6A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 2, 2, 2, 2], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 0, 0]]],
["nonPseudoParabolic","A^{2}_1+5A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2]]],
["nonPseudoParabolic","A^{1}_2+4A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["nonPseudoParabolic","B^{1}_2+4A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, -1, -1, -1, -1, -1], [0, 0, 1, 2, 2, 2, 2], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 0, 0]]],
["nonPseudoParabolic","A^{1}_3+3A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2]]],
["nonPseudoParabolic","A^{1}_3+A^{2}_1+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 1, 1, 1], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 0, 0]]],
["nonPseudoParabolic","2A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 0]]],
["nonPseudoParabolic","D^{1}_4+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 1, 0, 0]]],
["nonPseudoParabolic","A^{2}_1+6A^{1}_1", [[1, 1, 1, 1, 1, 1, 1], [0, 1, 2, 2, 2, 2, 2], [0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["nonPseudoParabolic","A^{1}_3+4A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["nonPseudoParabolic","A^{1}_3+B^{1}_2+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, -1, -1], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["nonPseudoParabolic","2A^{1}_3+A^{2}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1]]],
["nonPseudoParabolic","B^{1}_3+4A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, -1, -1, -1, -1], [0, 0, 0, 1, 2, 2, 2], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["nonPseudoParabolic","D^{1}_4+A^{2}_1+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 1, 1], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]],
["nonPseudoParabolic","D^{1}_4+A^{1}_3", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, -1, -2, -2, -2, -2], [0, 0, 0, 0, 1, 2, 2], [0, 0, 0, 0, 0, -1, 0], [0, 0, 0, 0, -1, 0, 0]]],
["nonPseudoParabolic","D^{1}_5+2A^{1}_1", [[1, 2, 2, 2, 2, 2, 2], [0, -1, 0, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0, 0], [0, 0, 0, -1, 0, 0, 0], [0, 0, 0, -1, -2, -2, -2], [0, 0, 0, 0, 0, 1, 2], [0, 0, 0, 0, 0, 1, 0]]]

LaTeX table with root subalgebra details.
\documentclass{article}
\usepackage{longtable, amssymb, lscape}
\begin{document}
Lie algebra type: $B^{1}_7$. There are 110 table entries (= 108 larger than the Cartan subalgebra + the Cartan subalgebra + the full subalgebra).
Let $\mathfrak g$ stand for the type of the regular subalgebra and $C(\mathfrak g)$ for the type of the centralizer. Let $r$ stand for the rank of $\mathfrak g$, let $r_c$ stand for the rank of the semisimple part of the centralizer, let $p$ stand for the number of positive roots of $\mathfrak g$, let $q$ stand for the number of positive roots of the centralizer, and let $m$ stand for the number of $A_1$ components (of all root lengths) of $\mathfrak g$. \begin{longtable}{cccccccc}
$\mathfrak g$ & $C(\mathfrak g)$& $p$ & $q$& $m$& $r$ & $c_r$ \\\endhead
$B^{1}_7$&$0$&$49$&$0$&$0$&$7$&$0$&\\
$D^{1}_7$&$0$&$42$&$0$&$0$&$7$&$0$&\\
$D^{1}_6+A^{2}_1$&$0$&$31$&$0$&$1$&$7$&$0$&\\
$B^{1}_5+2A^{1}_1$&$0$&$27$&$0$&$2$&$7$&$0$&\\
$D^{1}_5+B^{1}_2$&$0$&$24$&$0$&$0$&$7$&$0$&\\
$D^{1}_5+2A^{1}_1$&$0$&$22$&$0$&$2$&$7$&$0$&\\
$B^{1}_4+A^{1}_3$&$0$&$22$&$0$&$0$&$7$&$0$&\\
$D^{1}_4+B^{1}_3$&$0$&$21$&$0$&$0$&$7$&$0$&\\
$D^{1}_4+A^{1}_3$&$0$&$18$&$0$&$0$&$7$&$0$&\\
$D^{1}_4+A^{2}_1+2A^{1}_1$&$0$&$15$&$0$&$3$&$7$&$0$&\\
$B^{1}_3+4A^{1}_1$&$0$&$13$&$0$&$4$&$7$&$0$&\\
$2A^{1}_3+A^{2}_1$&$0$&$13$&$0$&$1$&$7$&$0$&\\
$A^{1}_3+B^{1}_2+2A^{1}_1$&$0$&$12$&$0$&$2$&$7$&$0$&\\
$A^{1}_3+4A^{1}_1$&$0$&$10$&$0$&$4$&$7$&$0$&\\
$A^{2}_1+6A^{1}_1$&$0$&$7$&$0$&$7$&$7$&$0$&\\
$B^{1}_6$&$0$&$36$&$0$&$0$&$6$&$0$&\\
$D^{1}_6$&$A^{2}_1$&$30$&$1$&$0$&$6$&$1$&\\
$A^{1}_6$&$0$&$21$&$0$&$0$&$6$&$0$&\\
$B^{1}_5+A^{1}_1$&$A^{1}_1$&$26$&$1$&$1$&$6$&$1$&\\
$D^{1}_5+A^{2}_1$&$0$&$21$&$0$&$1$&$6$&$0$&\\
$D^{1}_5+A^{1}_1$&$A^{1}_1$&$21$&$1$&$1$&$6$&$1$&\\
$A^{1}_5+A^{2}_1$&$0$&$16$&$0$&$1$&$6$&$0$&\\
$B^{1}_4+A^{1}_2$&$0$&$19$&$0$&$0$&$6$&$0$&\\
$B^{1}_4+2A^{1}_1$&$0$&$18$&$0$&$2$&$6$&$0$&\\
$D^{1}_4+B^{1}_2$&$0$&$16$&$0$&$0$&$6$&$0$&\\
$D^{1}_4+A^{1}_2$&$0$&$15$&$0$&$0$&$6$&$0$&\\
$D^{1}_4+A^{2}_1+A^{1}_1$&$A^{1}_1$&$14$&$1$&$2$&$6$&$1$&\\
$D^{1}_4+2A^{1}_1$&$A^{2}_1$&$14$&$1$&$2$&$6$&$1$&\\
$A^{1}_4+B^{1}_2$&$0$&$14$&$0$&$0$&$6$&$0$&\\
$A^{1}_4+2A^{1}_1$&$0$&$12$&$0$&$2$&$6$&$0$&\\
$B^{1}_3+A^{1}_3$&$0$&$15$&$0$&$0$&$6$&$0$&\\
$B^{1}_3+A^{1}_3$&$0$&$15$&$0$&$0$&$6$&$0$&\\
$B^{1}_3+3A^{1}_1$&$A^{1}_1$&$12$&$1$&$3$&$6$&$1$&\\
$2A^{1}_3$&$A^{2}_1$&$12$&$1$&$0$&$6$&$1$&\\
$2A^{1}_3$&$0$&$12$&$0$&$0$&$6$&$0$&\\
$A^{1}_3+B^{1}_2+A^{1}_1$&$A^{1}_1$&$11$&$1$&$1$&$6$&$1$&\\
$A^{1}_3+A^{1}_2+A^{2}_1$&$0$&$10$&$0$&$1$&$6$&$0$&\\
$A^{1}_3+A^{2}_1+2A^{1}_1$&$0$&$9$&$0$&$3$&$6$&$0$&\\
$A^{1}_3+A^{2}_1+2A^{1}_1$&$0$&$9$&$0$&$3$&$6$&$0$&\\
$A^{1}_3+3A^{1}_1$&$A^{1}_1$&$9$&$1$&$3$&$6$&$1$&\\
$B^{1}_2+A^{1}_2+2A^{1}_1$&$0$&$9$&$0$&$2$&$6$&$0$&\\
$B^{1}_2+4A^{1}_1$&$0$&$8$&$0$&$4$&$6$&$0$&\\
$A^{1}_2+4A^{1}_1$&$0$&$7$&$0$&$4$&$6$&$0$&\\
$A^{2}_1+5A^{1}_1$&$A^{1}_1$&$6$&$1$&$6$&$6$&$1$&\\
$6A^{1}_1$&$A^{2}_1$&$6$&$1$&$6$&$6$&$1$&\\
$B^{1}_5$&$2A^{1}_1$&$25$&$2$&$0$&$5$&$2$&\\
$D^{1}_5$&$B^{1}_2$&$20$&$4$&$0$&$5$&$2$&\\
$A^{1}_5$&$A^{2}_1$&$15$&$1$&$0$&$5$&$1$&\\
$B^{1}_4+A^{1}_1$&$A^{1}_1$&$17$&$1$&$1$&$5$&$1$&\\
$D^{1}_4+A^{2}_1$&$2A^{1}_1$&$13$&$2$&$1$&$5$&$2$&\\
$D^{1}_4+A^{1}_1$&$A^{2}_1+A^{1}_1$&$13$&$2$&$1$&$5$&$2$&\\
$A^{1}_4+A^{2}_1$&$0$&$11$&$0$&$1$&$5$&$0$&\\
$A^{1}_4+A^{1}_1$&$A^{1}_1$&$11$&$1$&$1$&$5$&$1$&\\
$B^{1}_3+A^{1}_2$&$0$&$12$&$0$&$0$&$5$&$0$&\\
$B^{1}_3+2A^{1}_1$&$2A^{1}_1$&$11$&$2$&$2$&$5$&$2$&\\
$B^{1}_3+2A^{1}_1$&$2A^{1}_1$&$11$&$2$&$2$&$5$&$2$&\\
$A^{1}_3+B^{1}_2$&$2A^{1}_1$&$10$&$2$&$0$&$5$&$2$&\\
$A^{1}_3+B^{1}_2$&$0$&$10$&$0$&$0$&$5$&$0$&\\
$A^{1}_3+A^{1}_2$&$A^{2}_1$&$9$&$1$&$0$&$5$&$1$&\\
$A^{1}_3+A^{1}_2$&$0$&$9$&$0$&$0$&$5$&$0$&\\
$A^{1}_3+A^{2}_1+A^{1}_1$&$A^{1}_1$&$8$&$1$&$2$&$5$&$1$&\\
$A^{1}_3+A^{2}_1+A^{1}_1$&$A^{1}_1$&$8$&$1$&$2$&$5$&$1$&\\
$A^{1}_3+2A^{1}_1$&$2A^{1}_1$&$8$&$2$&$2$&$5$&$2$&\\
$A^{1}_3+2A^{1}_1$&$A^{2}_1$&$8$&$1$&$2$&$5$&$1$&\\
$A^{1}_3+2A^{1}_1$&$B^{1}_2$&$8$&$4$&$2$&$5$&$2$&\\
$B^{1}_2+A^{1}_2+A^{1}_1$&$A^{1}_1$&$8$&$1$&$1$&$5$&$1$&\\
$B^{1}_2+3A^{1}_1$&$A^{1}_1$&$7$&$1$&$3$&$5$&$1$&\\
$2A^{1}_2+A^{2}_1$&$0$&$7$&$0$&$1$&$5$&$0$&\\
$A^{1}_2+A^{2}_1+2A^{1}_1$&$0$&$6$&$0$&$3$&$5$&$0$&\\
$A^{1}_2+3A^{1}_1$&$A^{1}_1$&$6$&$1$&$3$&$5$&$1$&\\
$A^{2}_1+4A^{1}_1$&$2A^{1}_1$&$5$&$2$&$5$&$5$&$2$&\\
$A^{2}_1+4A^{1}_1$&$2A^{1}_1$&$5$&$2$&$5$&$5$&$2$&\\
$5A^{1}_1$&$A^{2}_1+A^{1}_1$&$5$&$2$&$5$&$5$&$2$&\\
$B^{1}_4$&$A^{1}_3$&$16$&$6$&$0$&$4$&$3$&\\
$D^{1}_4$&$B^{1}_3$&$12$&$9$&$0$&$4$&$3$&\\
$A^{1}_4$&$B^{1}_2$&$10$&$4$&$0$&$4$&$2$&\\
$B^{1}_3+A^{1}_1$&$3A^{1}_1$&$10$&$3$&$1$&$4$&$3$&\\
$A^{1}_3+A^{2}_1$&$A^{1}_3$&$7$&$6$&$1$&$4$&$3$&\\
$A^{1}_3+A^{2}_1$&$2A^{1}_1$&$7$&$2$&$1$&$4$&$2$&\\
$A^{1}_3+A^{1}_1$&$B^{1}_2+A^{1}_1$&$7$&$5$&$1$&$4$&$3$&\\
$A^{1}_3+A^{1}_1$&$A^{2}_1+A^{1}_1$&$7$&$2$&$1$&$4$&$2$&\\
$B^{1}_2+A^{1}_2$&$2A^{1}_1$&$7$&$2$&$0$&$4$&$2$&\\
$B^{1}_2+2A^{1}_1$&$A^{1}_3$&$6$&$6$&$2$&$4$&$3$&\\
$B^{1}_2+2A^{1}_1$&$2A^{1}_1$&$6$&$2$&$2$&$4$&$2$&\\
$2A^{1}_2$&$A^{2}_1$&$6$&$1$&$0$&$4$&$1$&\\
$A^{1}_2+A^{2}_1+A^{1}_1$&$A^{1}_1$&$5$&$1$&$2$&$4$&$1$&\\
$A^{1}_2+2A^{1}_1$&$2A^{1}_1$&$5$&$2$&$2$&$4$&$2$&\\
$A^{1}_2+2A^{1}_1$&$B^{1}_2$&$5$&$4$&$2$&$4$&$2$&\\
$A^{2}_1+3A^{1}_1$&$3A^{1}_1$&$4$&$3$&$4$&$4$&$3$&\\
$A^{2}_1+3A^{1}_1$&$3A^{1}_1$&$4$&$3$&$4$&$4$&$3$&\\
$4A^{1}_1$&$B^{1}_3$&$4$&$9$&$4$&$4$&$3$&\\
$4A^{1}_1$&$A^{2}_1+2A^{1}_1$&$4$&$3$&$4$&$4$&$3$&\\
$B^{1}_3$&$D^{1}_4$&$9$&$12$&$0$&$3$&$4$&\\
$A^{1}_3$&$B^{1}_3$&$6$&$9$&$0$&$3$&$3$&\\
$A^{1}_3$&$B^{1}_4$&$6$&$16$&$0$&$3$&$4$&\\
$B^{1}_2+A^{1}_1$&$A^{1}_3+A^{1}_1$&$5$&$7$&$1$&$3$&$4$&\\
$A^{1}_2+A^{2}_1$&$A^{1}_3$&$4$&$6$&$1$&$3$&$3$&\\
$A^{1}_2+A^{1}_1$&$B^{1}_2+A^{1}_1$&$4$&$5$&$1$&$3$&$3$&\\
$A^{2}_1+2A^{1}_1$&$D^{1}_4$&$3$&$12$&$3$&$3$&$4$&\\
$A^{2}_1+2A^{1}_1$&$4A^{1}_1$&$3$&$4$&$3$&$3$&$4$&\\
$3A^{1}_1$&$A^{2}_1+3A^{1}_1$&$3$&$4$&$3$&$3$&$4$&\\
$3A^{1}_1$&$B^{1}_3+A^{1}_1$&$3$&$10$&$3$&$3$&$4$&\\
$B^{1}_2$&$D^{1}_5$&$4$&$20$&$0$&$2$&$5$&\\
$A^{1}_2$&$B^{1}_4$&$3$&$16$&$0$&$2$&$4$&\\
$A^{2}_1+A^{1}_1$&$D^{1}_4+A^{1}_1$&$2$&$13$&$2$&$2$&$5$&\\
$2A^{1}_1$&$B^{1}_3+2A^{1}_1$&$2$&$11$&$2$&$2$&$5$&\\
$2A^{1}_1$&$B^{1}_5$&$2$&$25$&$2$&$2$&$5$&\\
$A^{2}_1$&$D^{1}_6$&$1$&$30$&$1$&$1$&$6$&\\
$A^{1}_1$&$B^{1}_5+A^{1}_1$&$1$&$26$&$1$&$1$&$6$&\\
$0$&$B^{1}_7$&$0$&$49$&$0$&$0$&$7$&\\
\end{longtable}
\end{document}