Type: \(\displaystyle E^{1}_6\) (Dynkin type computed to be: \(\displaystyle E^{1}_6\))
Simple basis: 6 vectors: (2, 3, 4, 6, 5, 4, 3, 2), (0, -1, -1, -2, -2, -1, 0, 0), (0, 0, 0, 0, 0, 0, 0, -1), (0, 0, 0, 0, 0, 0, -1, 0), (0, 0, 0, 0, 0, -1, 0, 0), (-1, 0, -1, -1, -1, 0, 0, 0)
Simple basis epsilon form:
Simple basis epsilon form with respect to k:
Number of outer autos with trivial action on orthogonal complement and extending to autos of ambient algebra: 0
Number of outer autos with trivial action on orthogonal complement: 0.
C(k_{ss})_{ss}: A^{1}_2
simple basis centralizer: 2 vectors: (0, 0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0, 0)
Number of k-submodules of g: 15
Module decomposition, fundamental coords over k: \(\displaystyle 3V_{\omega_{6}}+V_{\omega_{2}}+3V_{\omega_{1}}+8V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, 0, -1, -1, 0, 0, 0, 0)(0, 0, -1, -1, 0, 0, 0, 0)g_{-11}-\varepsilon_{1}+\varepsilon_{3}
Module 21(0, 0, 0, -1, 0, 0, 0, 0)(0, 0, 0, -1, 0, 0, 0, 0)g_{-4}-\varepsilon_{2}+\varepsilon_{3}
Module 31(0, 0, -1, 0, 0, 0, 0, 0)(0, 0, -1, 0, 0, 0, 0, 0)g_{-3}-\varepsilon_{1}+\varepsilon_{2}
Module 427(-2, -3, -4, -6, -4, -3, -2, -1)(0, 1, 0, 0, 0, 0, 0, 0)g_{2}
g_{30}
g_{38}
g_{47}
g_{85}
g_{55}
g_{-110}
g_{90}
g_{-88}
g_{95}
g_{-83}
g_{100}
g_{-76}
g_{-77}
g_{109}
g_{-70}
g_{-56}
g_{-63}
g_{-48}
g_{-16}
g_{-39}
g_{5}
g_{-31}
g_{13}
g_{21}
g_{29}
g_{-116}		-\varepsilon_{1}-\varepsilon_{2}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{3}-\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{3}+\varepsilon_{7}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{3}+\varepsilon_{6}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{3}+\varepsilon_{5}
\varepsilon_{3}-\varepsilon_{4}
\varepsilon_{3}+\varepsilon_{4}
\varepsilon_{3}-\varepsilon_{5}
\varepsilon_{3}-\varepsilon_{6}
\varepsilon_{3}-\varepsilon_{7}
\varepsilon_{3}+\varepsilon_{8}
Module 51(0, 0, 1, 0, 0, 0, 0, 0)(0, 0, 1, 0, 0, 0, 0, 0)g_{3}\varepsilon_{1}-\varepsilon_{2}
Module 61(0, 0, 0, 1, 0, 0, 0, 0)(0, 0, 0, 1, 0, 0, 0, 0)g_{4}\varepsilon_{2}-\varepsilon_{3}
Module 727(-2, -3, -4, -5, -4, -3, -2, -1)(0, 1, 0, 1, 0, 0, 0, 0)g_{10}
g_{37}
g_{45}
g_{53}
g_{89}
g_{61}
g_{-108}
g_{94}
g_{-84}
g_{99}
g_{-78}
g_{103}
g_{-71}
g_{-72}
g_{111}
g_{-64}
g_{-50}
g_{-57}
g_{-41}
g_{-9}
g_{-33}
g_{12}
g_{-25}
g_{20}
g_{28}
g_{36}
g_{-115}		-\varepsilon_{1}-\varepsilon_{3}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}-\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{7}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{6}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{5}
\varepsilon_{2}-\varepsilon_{4}
\varepsilon_{2}+\varepsilon_{4}
\varepsilon_{2}-\varepsilon_{5}
\varepsilon_{2}-\varepsilon_{6}
\varepsilon_{2}-\varepsilon_{7}
\varepsilon_{2}+\varepsilon_{8}
Module 81(0, 0, 1, 1, 0, 0, 0, 0)(0, 0, 1, 1, 0, 0, 0, 0)g_{11}\varepsilon_{1}-\varepsilon_{3}
Module 927(-2, -3, -3, -5, -4, -3, -2, -1)(0, 1, 1, 1, 0, 0, 0, 0)g_{17}
g_{44}
g_{51}
g_{58}
g_{93}
g_{66}
g_{-106}
g_{98}
g_{-79}
g_{102}
g_{-73}
g_{105}
g_{-65}
g_{-67}
g_{114}
g_{-59}
g_{-42}
g_{-52}
g_{-34}
g_{-1}
g_{-26}
g_{19}
g_{-18}
g_{27}
g_{35}
g_{43}
g_{-113}		-\varepsilon_{2}-\varepsilon_{3}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{1}-\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{1}+\varepsilon_{7}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{1}+\varepsilon_{6}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{1}+\varepsilon_{5}
\varepsilon_{1}-\varepsilon_{4}
\varepsilon_{1}+\varepsilon_{4}
\varepsilon_{1}-\varepsilon_{5}
\varepsilon_{1}-\varepsilon_{6}
\varepsilon_{1}-\varepsilon_{7}
\varepsilon_{1}+\varepsilon_{8}
Module 1078(-1, -1, -1, -1, 0, 0, 0, 0)(1, 1, 1, 1, 0, 0, 0, 0)g_{23}
g_{69}
g_{75}
g_{82}
g_{80}
g_{-96}
g_{86}
g_{97}
g_{-92}
g_{91}
g_{101}
g_{-87}
g_{112}
g_{-74}
g_{104}
g_{-49}
g_{-81}
g_{-68}
g_{117}
g_{107}
g_{-40}
g_{-22}
g_{-60}
g_{-62}
g_{118}
g_{-32}
g_{-14}
g_{-15}
g_{-54}
g_{119}
g_{-24}
g_{-6}
g_{-7}
g_{-8}
g_{-46}
g_{120}
-h_{5}-h_{4}-h_{3}-h_{1}
-h_{6}
-h_{7}
-h_{8}
-h_{6}-2h_{5}-2h_{4}-h_{3}-h_{2}
2h_{8}+3h_{7}+4h_{6}+5h_{5}+6h_{4}+4h_{3}+3h_{2}+2h_{1}
g_{-120}
g_{46}
g_{8}
g_{7}
g_{6}
g_{24}
g_{-119}
g_{54}
g_{15}
g_{14}
g_{32}
g_{-118}
g_{62}
g_{60}
g_{22}
g_{40}
g_{-107}
g_{-117}
g_{68}
g_{81}
g_{49}
g_{-104}
g_{74}
g_{-112}
g_{87}
g_{-101}
g_{-91}
g_{92}
g_{-97}
g_{-86}
g_{96}
g_{-80}
g_{-82}
g_{-75}
g_{-69}
g_{-23}		-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
\varepsilon_{7}-\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
\varepsilon_{6}-\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
\varepsilon_{6}+\varepsilon_{7}
\varepsilon_{5}-\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{5}+\varepsilon_{7}
-\varepsilon_{4}-\varepsilon_{8}
\varepsilon_{4}-\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{4}+\varepsilon_{7}
\varepsilon_{5}+\varepsilon_{6}
\varepsilon_{4}+\varepsilon_{7}
-\varepsilon_{5}-\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{4}+\varepsilon_{6}
-\varepsilon_{5}+\varepsilon_{7}
\varepsilon_{4}+\varepsilon_{6}
-\varepsilon_{6}-\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{4}+\varepsilon_{5}
-\varepsilon_{5}+\varepsilon_{6}
-\varepsilon_{6}+\varepsilon_{7}
\varepsilon_{4}+\varepsilon_{5}
-\varepsilon_{7}-\varepsilon_{8}
0
0
0
0
0
0
\varepsilon_{7}+\varepsilon_{8}
-\varepsilon_{4}-\varepsilon_{5}
\varepsilon_{6}-\varepsilon_{7}
\varepsilon_{5}-\varepsilon_{6}
\varepsilon_{4}-\varepsilon_{5}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
\varepsilon_{6}+\varepsilon_{8}
-\varepsilon_{4}-\varepsilon_{6}
\varepsilon_{5}-\varepsilon_{7}
\varepsilon_{4}-\varepsilon_{6}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
\varepsilon_{5}+\varepsilon_{8}
-\varepsilon_{4}-\varepsilon_{7}
-\varepsilon_{5}-\varepsilon_{6}
\varepsilon_{4}-\varepsilon_{7}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{4}+\varepsilon_{8}
\varepsilon_{4}+\varepsilon_{8}
-\varepsilon_{5}-\varepsilon_{7}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{5}+\varepsilon_{8}
-\varepsilon_{6}-\varepsilon_{7}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{6}+\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{7}+\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 1127(0, -1, -1, -1, 0, 0, 0, 0)(2, 3, 3, 5, 4, 3, 2, 1)g_{113}
g_{-43}
g_{-35}
g_{-27}
g_{18}
g_{-19}
g_{26}
g_{1}
g_{34}
g_{52}
g_{42}
g_{59}
g_{-114}
g_{67}
g_{65}
g_{-105}
g_{73}
g_{-102}
g_{79}
g_{-98}
g_{106}
g_{-66}
g_{-93}
g_{-58}
g_{-51}
g_{-44}
g_{-17}		-\varepsilon_{1}-\varepsilon_{8}
-\varepsilon_{1}+\varepsilon_{7}
-\varepsilon_{1}+\varepsilon_{6}
-\varepsilon_{1}+\varepsilon_{5}
-\varepsilon_{1}-\varepsilon_{4}
-\varepsilon_{1}+\varepsilon_{4}
-\varepsilon_{1}-\varepsilon_{5}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{1}-\varepsilon_{6}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{1}-\varepsilon_{7}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{1}+\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{3}
Module 1227(0, -1, 0, -1, 0, 0, 0, 0)(2, 3, 4, 5, 4, 3, 2, 1)g_{115}
g_{-36}
g_{-28}
g_{-20}
g_{25}
g_{-12}
g_{33}
g_{9}
g_{41}
g_{57}
g_{50}
g_{64}
g_{-111}
g_{72}
g_{71}
g_{-103}
g_{78}
g_{-99}
g_{84}
g_{-94}
g_{108}
g_{-61}
g_{-89}
g_{-53}
g_{-45}
g_{-37}
g_{-10}		-\varepsilon_{2}-\varepsilon_{8}
-\varepsilon_{2}+\varepsilon_{7}
-\varepsilon_{2}+\varepsilon_{6}
-\varepsilon_{2}+\varepsilon_{5}
-\varepsilon_{2}-\varepsilon_{4}
-\varepsilon_{2}+\varepsilon_{4}
-\varepsilon_{2}-\varepsilon_{5}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{2}-\varepsilon_{6}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{2}-\varepsilon_{7}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{2}+\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{1}+\varepsilon_{3}
Module 1327(0, -1, 0, 0, 0, 0, 0, 0)(2, 3, 4, 6, 4, 3, 2, 1)g_{116}
g_{-29}
g_{-21}
g_{-13}
g_{31}
g_{-5}
g_{39}
g_{16}
g_{48}
g_{63}
g_{56}
g_{70}
g_{-109}
g_{77}
g_{76}
g_{-100}
g_{83}
g_{-95}
g_{88}
g_{-90}
g_{110}
g_{-55}
g_{-85}
g_{-47}
g_{-38}
g_{-30}
g_{-2}		-\varepsilon_{3}-\varepsilon_{8}
-\varepsilon_{3}+\varepsilon_{7}
-\varepsilon_{3}+\varepsilon_{6}
-\varepsilon_{3}+\varepsilon_{5}
-\varepsilon_{3}-\varepsilon_{4}
-\varepsilon_{3}+\varepsilon_{4}
-\varepsilon_{3}-\varepsilon_{5}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{3}-\varepsilon_{6}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{3}-\varepsilon_{7}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-\varepsilon_{3}+\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{1}+\varepsilon_{2}
Module 141(0, 0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0, 0)h_{3}0
Module 151(0, 0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0, 0)h_{4}0
Information about the subalgebra generation algorithm.
Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 4
Heirs rejected due to not being maximally dominant: 7
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 7
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
Parabolically induced by D^{1}_5
Potential Dynkin type extensions: E^{1}_7, E^{1}_6+A^{1}_1,