Type: \(\displaystyle 3A^{1}_1\) (Dynkin type computed to be: \(\displaystyle 3A^{1}_1\))
Simple basis: 3 vectors: (2, 2, 3, 4, 3, 2, 1), (0, 1, 1, 2, 2, 2, 1), (0, 0, 0, 0, 0, 0, 1)
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}: D^{1}_4
simple basis centralizer: 4 vectors: (0, 0, 0, 1, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0)
Number of k-submodules of g: 55
Module decomposition, fundamental coords over k: \(\displaystyle V_{2\omega_{3}}+8V_{\omega_{2}+\omega_{3}}+8V_{\omega_{1}+\omega_{3}}+V_{2\omega_{2}}+8V_{\omega_{1}+\omega_{2}}+V_{2\omega_{1}}+28V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, -1, -1, -2, -1, 0, 0)(0, -1, -1, -2, -1, 0, 0)g_{-27}\varepsilon_{3}+\varepsilon_{4}
Module 21(0, -1, -1, -1, -1, 0, 0)(0, -1, -1, -1, -1, 0, 0)g_{-22}\varepsilon_{2}+\varepsilon_{4}
Module 31(0, 0, -1, -1, -1, 0, 0)(0, 0, -1, -1, -1, 0, 0)g_{-17}-\varepsilon_{1}+\varepsilon_{4}
Module 41(0, -1, 0, -1, -1, 0, 0)(0, -1, 0, -1, -1, 0, 0)g_{-16}\varepsilon_{1}+\varepsilon_{4}
Module 51(0, -1, -1, -1, 0, 0, 0)(0, -1, -1, -1, 0, 0, 0)g_{-15}\varepsilon_{2}+\varepsilon_{3}
Module 61(0, 0, 0, -1, -1, 0, 0)(0, 0, 0, -1, -1, 0, 0)g_{-11}-\varepsilon_{2}+\varepsilon_{4}
Module 71(0, 0, -1, -1, 0, 0, 0)(0, 0, -1, -1, 0, 0, 0)g_{-10}-\varepsilon_{1}+\varepsilon_{3}
Module 81(0, -1, 0, -1, 0, 0, 0)(0, -1, 0, -1, 0, 0, 0)g_{-9}\varepsilon_{1}+\varepsilon_{3}
Module 91(0, 0, 0, 0, -1, 0, 0)(0, 0, 0, 0, -1, 0, 0)g_{-5}-\varepsilon_{3}+\varepsilon_{4}
Module 101(0, 0, 0, -1, 0, 0, 0)(0, 0, 0, -1, 0, 0, 0)g_{-4}-\varepsilon_{2}+\varepsilon_{3}
Module 111(0, 0, -1, 0, 0, 0, 0)(0, 0, -1, 0, 0, 0, 0)g_{-3}-\varepsilon_{1}+\varepsilon_{2}
Module 121(0, -1, 0, 0, 0, 0, 0)(0, -1, 0, 0, 0, 0, 0)g_{-2}\varepsilon_{1}+\varepsilon_{2}
Module 131(0, 1, 0, 0, 0, 0, 0)(0, 1, 0, 0, 0, 0, 0)g_{2}-\varepsilon_{1}-\varepsilon_{2}
Module 141(0, 0, 1, 0, 0, 0, 0)(0, 0, 1, 0, 0, 0, 0)g_{3}\varepsilon_{1}-\varepsilon_{2}
Module 151(0, 0, 0, 1, 0, 0, 0)(0, 0, 0, 1, 0, 0, 0)g_{4}\varepsilon_{2}-\varepsilon_{3}
Module 161(0, 0, 0, 0, 1, 0, 0)(0, 0, 0, 0, 1, 0, 0)g_{5}\varepsilon_{3}-\varepsilon_{4}
Module 173(0, 0, 0, 0, 0, 0, -1)(0, 0, 0, 0, 0, 0, 1)g_{7}
h_{7}
g_{-7}		\varepsilon_{5}-\varepsilon_{6}
0
-\varepsilon_{5}+\varepsilon_{6}
Module 181(0, 1, 0, 1, 0, 0, 0)(0, 1, 0, 1, 0, 0, 0)g_{9}-\varepsilon_{1}-\varepsilon_{3}
Module 191(0, 0, 1, 1, 0, 0, 0)(0, 0, 1, 1, 0, 0, 0)g_{10}\varepsilon_{1}-\varepsilon_{3}
Module 201(0, 0, 0, 1, 1, 0, 0)(0, 0, 0, 1, 1, 0, 0)g_{11}\varepsilon_{2}-\varepsilon_{4}
Module 214(0, -1, -1, -2, -2, -1, -1)(0, 0, 0, 0, 0, 1, 1)g_{13}
g_{-39}
g_{6}
g_{-45}		\varepsilon_{4}-\varepsilon_{6}
\varepsilon_{4}+\varepsilon_{5}
\varepsilon_{4}-\varepsilon_{5}
\varepsilon_{4}+\varepsilon_{6}
Module 221(0, 1, 1, 1, 0, 0, 0)(0, 1, 1, 1, 0, 0, 0)g_{15}-\varepsilon_{2}-\varepsilon_{3}
Module 231(0, 1, 0, 1, 1, 0, 0)(0, 1, 0, 1, 1, 0, 0)g_{16}-\varepsilon_{1}-\varepsilon_{4}
Module 241(0, 0, 1, 1, 1, 0, 0)(0, 0, 1, 1, 1, 0, 0)g_{17}\varepsilon_{1}-\varepsilon_{4}
Module 254(0, -1, -1, -2, -1, -1, -1)(0, 0, 0, 0, 1, 1, 1)g_{19}
g_{-34}
g_{12}
g_{-41}		\varepsilon_{3}-\varepsilon_{6}
\varepsilon_{3}+\varepsilon_{5}
\varepsilon_{3}-\varepsilon_{5}
\varepsilon_{3}+\varepsilon_{6}
Module 261(0, 1, 1, 1, 1, 0, 0)(0, 1, 1, 1, 1, 0, 0)g_{22}-\varepsilon_{2}-\varepsilon_{4}
Module 274(0, -1, -1, -1, -1, -1, -1)(0, 0, 0, 1, 1, 1, 1)g_{25}
g_{-29}
g_{18}
g_{-36}		\varepsilon_{2}-\varepsilon_{6}
\varepsilon_{2}+\varepsilon_{5}
\varepsilon_{2}-\varepsilon_{5}
\varepsilon_{2}+\varepsilon_{6}
Module 281(0, 1, 1, 2, 1, 0, 0)(0, 1, 1, 2, 1, 0, 0)g_{27}-\varepsilon_{3}-\varepsilon_{4}
Module 294(0, 0, -1, -1, -1, -1, -1)(0, 1, 0, 1, 1, 1, 1)g_{30}
g_{-24}
g_{23}
g_{-31}		-\varepsilon_{1}-\varepsilon_{6}
-\varepsilon_{1}+\varepsilon_{5}
-\varepsilon_{1}-\varepsilon_{5}
-\varepsilon_{1}+\varepsilon_{6}
Module 304(0, -1, 0, -1, -1, -1, -1)(0, 0, 1, 1, 1, 1, 1)g_{31}
g_{-23}
g_{24}
g_{-30}		\varepsilon_{1}-\varepsilon_{6}
\varepsilon_{1}+\varepsilon_{5}
\varepsilon_{1}-\varepsilon_{5}
\varepsilon_{1}+\varepsilon_{6}
Module 314(-1, -2, -2, -3, -2, -1, -1)(1, 0, 1, 1, 1, 1, 1)g_{35}
g_{-53}
g_{28}
g_{-56}		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 324(0, 0, 0, -1, -1, -1, -1)(0, 1, 1, 1, 1, 1, 1)g_{36}
g_{-18}
g_{29}
g_{-25}		-\varepsilon_{2}-\varepsilon_{6}
-\varepsilon_{2}+\varepsilon_{5}
-\varepsilon_{2}-\varepsilon_{5}
-\varepsilon_{2}+\varepsilon_{6}
Module 334(-1, -1, -2, -3, -2, -1, -1)(1, 1, 1, 1, 1, 1, 1)g_{40}
g_{-50}
g_{33}
g_{-54}		-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 344(0, 0, 0, 0, -1, -1, -1)(0, 1, 1, 2, 1, 1, 1)g_{41}
g_{-12}
g_{34}
g_{-19}		-\varepsilon_{3}-\varepsilon_{6}
-\varepsilon_{3}+\varepsilon_{5}
-\varepsilon_{3}-\varepsilon_{5}
-\varepsilon_{3}+\varepsilon_{6}
Module 354(-1, -1, -2, -2, -2, -1, -1)(1, 1, 1, 2, 1, 1, 1)g_{44}
g_{-46}
g_{38}
g_{-51}		-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 364(0, 0, 0, 0, 0, -1, -1)(0, 1, 1, 2, 2, 1, 1)g_{45}
g_{-6}
g_{39}
g_{-13}		-\varepsilon_{4}-\varepsilon_{6}
-\varepsilon_{4}+\varepsilon_{5}
-\varepsilon_{4}-\varepsilon_{5}
-\varepsilon_{4}+\varepsilon_{6}
Module 374(-1, -1, -1, -2, -2, -1, -1)(1, 1, 2, 2, 1, 1, 1)g_{47}
g_{-43}
g_{42}
g_{-48}		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 384(-1, -1, -2, -2, -1, -1, -1)(1, 1, 1, 2, 2, 1, 1)g_{48}
g_{-42}
g_{43}
g_{-47}		-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 393(0, -1, -1, -2, -2, -2, -1)(0, 1, 1, 2, 2, 2, 1)g_{49}
h_{7}+2h_{6}+2h_{5}+2h_{4}+h_{3}+h_{2}
g_{-49}		-\varepsilon_{5}-\varepsilon_{6}
0
\varepsilon_{5}+\varepsilon_{6}
Module 404(-1, -1, -1, -2, -1, -1, -1)(1, 1, 2, 2, 2, 1, 1)g_{51}
g_{-38}
g_{46}
g_{-44}		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 414(-1, -2, -3, -4, -3, -2, -1)(1, 1, 1, 2, 2, 2, 1)g_{52}
g_{-37}
g_{1}
g_{-62}		-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 424(-1, -1, -1, -1, -1, -1, -1)(1, 1, 2, 3, 2, 1, 1)g_{54}
g_{-33}
g_{50}
g_{-40}		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 434(-1, -2, -2, -4, -3, -2, -1)(1, 1, 2, 2, 2, 2, 1)g_{55}
g_{-32}
g_{8}
g_{-61}		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 444(-1, 0, -1, -1, -1, -1, -1)(1, 2, 2, 3, 2, 1, 1)g_{56}
g_{-28}
g_{53}
g_{-35}		-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 454(-1, -2, -2, -3, -3, -2, -1)(1, 1, 2, 3, 2, 2, 1)g_{57}
g_{-26}
g_{14}
g_{-60}		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 464(-1, -1, -2, -3, -3, -2, -1)(1, 2, 2, 3, 2, 2, 1)g_{58}
g_{-21}
g_{20}
g_{-59}		-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 474(-1, -2, -2, -3, -2, -2, -1)(1, 1, 2, 3, 3, 2, 1)g_{59}
g_{-20}
g_{21}
g_{-58}		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 484(-1, -1, -2, -3, -2, -2, -1)(1, 2, 2, 3, 3, 2, 1)g_{60}
g_{-14}
g_{26}
g_{-57}		-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 494(-1, -1, -2, -2, -2, -2, -1)(1, 2, 2, 4, 3, 2, 1)g_{61}
g_{-8}
g_{32}
g_{-55}		-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 504(-1, -1, -1, -2, -2, -2, -1)(1, 2, 3, 4, 3, 2, 1)g_{62}
g_{-1}
g_{37}
g_{-52}		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 513(-2, -2, -3, -4, -3, -2, -1)(2, 2, 3, 4, 3, 2, 1)g_{63}
h_{7}+2h_{6}+3h_{5}+4h_{4}+3h_{3}+2h_{2}+2h_{1}
g_{-63}		\varepsilon_{7}-\varepsilon_{8}
0
-\varepsilon_{7}+\varepsilon_{8}
Module 521(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{2}0
Module 531(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{3}0
Module 541(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{4}0
Module 551(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{5}0
Information about the subalgebra generation algorithm.
Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 27
Heirs rejected due to not being maximally dominant: 23
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 23
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
Parabolically induced by 2A^{1}_1
Potential Dynkin type extensions: 4A^{1}_1,