Type: \(\displaystyle 2A^{1}_1\) (Dynkin type computed to be: \(\displaystyle 2A^{1}_1\))
Simple basis: 2 vectors: (2, 2, 3, 4, 3, 2, 1), (0, 1, 1, 2, 2, 2, 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+A^{1}_1
simple basis centralizer: 5 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), (0, 0, 0, 0, 0, 0, 1)
Number of k-submodules of g: 73
Module decomposition, fundamental coords over k: \(\displaystyle V_{2\omega_{2}}+8V_{\omega_{1}+\omega_{2}}+V_{2\omega_{1}}+16V_{\omega_{2}}+16V_{\omega_{1}}+31V_{0}\)
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, 0, 0, -1)(0, 0, 0, 0, 0, 0, -1)g_{-7}-\varepsilon_{5}+\varepsilon_{6}
Module 101(0, 0, 0, 0, -1, 0, 0)(0, 0, 0, 0, -1, 0, 0)g_{-5}-\varepsilon_{3}+\varepsilon_{4}
Module 111(0, 0, 0, -1, 0, 0, 0)(0, 0, 0, -1, 0, 0, 0)g_{-4}-\varepsilon_{2}+\varepsilon_{3}
Module 121(0, 0, -1, 0, 0, 0, 0)(0, 0, -1, 0, 0, 0, 0)g_{-3}-\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, 1, 0, 0, 0, 0, 0)(0, 1, 0, 0, 0, 0, 0)g_{2}-\varepsilon_{1}-\varepsilon_{2}
Module 151(0, 0, 1, 0, 0, 0, 0)(0, 0, 1, 0, 0, 0, 0)g_{3}\varepsilon_{1}-\varepsilon_{2}
Module 161(0, 0, 0, 1, 0, 0, 0)(0, 0, 0, 1, 0, 0, 0)g_{4}\varepsilon_{2}-\varepsilon_{3}
Module 171(0, 0, 0, 0, 1, 0, 0)(0, 0, 0, 0, 1, 0, 0)g_{5}\varepsilon_{3}-\varepsilon_{4}
Module 182(0, -1, -1, -2, -2, -1, -1)(0, 0, 0, 0, 0, 1, 0)g_{6}
g_{-45}		\varepsilon_{4}-\varepsilon_{5}
\varepsilon_{4}+\varepsilon_{6}
Module 191(0, 0, 0, 0, 0, 0, 1)(0, 0, 0, 0, 0, 0, 1)g_{7}\varepsilon_{5}-\varepsilon_{6}
Module 201(0, 1, 0, 1, 0, 0, 0)(0, 1, 0, 1, 0, 0, 0)g_{9}-\varepsilon_{1}-\varepsilon_{3}
Module 211(0, 0, 1, 1, 0, 0, 0)(0, 0, 1, 1, 0, 0, 0)g_{10}\varepsilon_{1}-\varepsilon_{3}
Module 221(0, 0, 0, 1, 1, 0, 0)(0, 0, 0, 1, 1, 0, 0)g_{11}\varepsilon_{2}-\varepsilon_{4}
Module 232(0, -1, -1, -2, -1, -1, -1)(0, 0, 0, 0, 1, 1, 0)g_{12}
g_{-41}		\varepsilon_{3}-\varepsilon_{5}
\varepsilon_{3}+\varepsilon_{6}
Module 242(0, -1, -1, -2, -2, -1, 0)(0, 0, 0, 0, 0, 1, 1)g_{13}
g_{-39}		\varepsilon_{4}-\varepsilon_{6}
\varepsilon_{4}+\varepsilon_{5}
Module 251(0, 1, 1, 1, 0, 0, 0)(0, 1, 1, 1, 0, 0, 0)g_{15}-\varepsilon_{2}-\varepsilon_{3}
Module 261(0, 1, 0, 1, 1, 0, 0)(0, 1, 0, 1, 1, 0, 0)g_{16}-\varepsilon_{1}-\varepsilon_{4}
Module 271(0, 0, 1, 1, 1, 0, 0)(0, 0, 1, 1, 1, 0, 0)g_{17}\varepsilon_{1}-\varepsilon_{4}
Module 282(0, -1, -1, -1, -1, -1, -1)(0, 0, 0, 1, 1, 1, 0)g_{18}
g_{-36}		\varepsilon_{2}-\varepsilon_{5}
\varepsilon_{2}+\varepsilon_{6}
Module 292(0, -1, -1, -2, -1, -1, 0)(0, 0, 0, 0, 1, 1, 1)g_{19}
g_{-34}		\varepsilon_{3}-\varepsilon_{6}
\varepsilon_{3}+\varepsilon_{5}
Module 301(0, 1, 1, 1, 1, 0, 0)(0, 1, 1, 1, 1, 0, 0)g_{22}-\varepsilon_{2}-\varepsilon_{4}
Module 312(0, 0, -1, -1, -1, -1, -1)(0, 1, 0, 1, 1, 1, 0)g_{23}
g_{-31}		-\varepsilon_{1}-\varepsilon_{5}
-\varepsilon_{1}+\varepsilon_{6}
Module 322(0, -1, 0, -1, -1, -1, -1)(0, 0, 1, 1, 1, 1, 0)g_{24}
g_{-30}		\varepsilon_{1}-\varepsilon_{5}
\varepsilon_{1}+\varepsilon_{6}
Module 332(0, -1, -1, -1, -1, -1, 0)(0, 0, 0, 1, 1, 1, 1)g_{25}
g_{-29}		\varepsilon_{2}-\varepsilon_{6}
\varepsilon_{2}+\varepsilon_{5}
Module 341(0, 1, 1, 2, 1, 0, 0)(0, 1, 1, 2, 1, 0, 0)g_{27}-\varepsilon_{3}-\varepsilon_{4}
Module 352(-1, -2, -2, -3, -2, -1, -1)(1, 0, 1, 1, 1, 1, 0)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}
Module 362(0, 0, 0, -1, -1, -1, -1)(0, 1, 1, 1, 1, 1, 0)g_{29}
g_{-25}		-\varepsilon_{2}-\varepsilon_{5}
-\varepsilon_{2}+\varepsilon_{6}
Module 372(0, 0, -1, -1, -1, -1, 0)(0, 1, 0, 1, 1, 1, 1)g_{30}
g_{-24}		-\varepsilon_{1}-\varepsilon_{6}
-\varepsilon_{1}+\varepsilon_{5}
Module 382(0, -1, 0, -1, -1, -1, 0)(0, 0, 1, 1, 1, 1, 1)g_{31}
g_{-23}		\varepsilon_{1}-\varepsilon_{6}
\varepsilon_{1}+\varepsilon_{5}
Module 392(-1, -1, -2, -3, -2, -1, -1)(1, 1, 1, 1, 1, 1, 0)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}
Module 402(0, 0, 0, 0, -1, -1, -1)(0, 1, 1, 2, 1, 1, 0)g_{34}
g_{-19}		-\varepsilon_{3}-\varepsilon_{5}
-\varepsilon_{3}+\varepsilon_{6}
Module 412(-1, -2, -2, -3, -2, -1, 0)(1, 0, 1, 1, 1, 1, 1)g_{35}
g_{-53}		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 422(0, 0, 0, -1, -1, -1, 0)(0, 1, 1, 1, 1, 1, 1)g_{36}
g_{-18}		-\varepsilon_{2}-\varepsilon_{6}
-\varepsilon_{2}+\varepsilon_{5}
Module 432(-1, -1, -2, -2, -2, -1, -1)(1, 1, 1, 2, 1, 1, 0)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}
Module 442(0, 0, 0, 0, 0, -1, -1)(0, 1, 1, 2, 2, 1, 0)g_{39}
g_{-13}		-\varepsilon_{4}-\varepsilon_{5}
-\varepsilon_{4}+\varepsilon_{6}
Module 452(-1, -1, -2, -3, -2, -1, 0)(1, 1, 1, 1, 1, 1, 1)g_{40}
g_{-50}		-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 462(0, 0, 0, 0, -1, -1, 0)(0, 1, 1, 2, 1, 1, 1)g_{41}
g_{-12}		-\varepsilon_{3}-\varepsilon_{6}
-\varepsilon_{3}+\varepsilon_{5}
Module 472(-1, -1, -1, -2, -2, -1, -1)(1, 1, 2, 2, 1, 1, 0)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}
Module 482(-1, -1, -2, -2, -1, -1, -1)(1, 1, 1, 2, 2, 1, 0)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}
Module 492(-1, -1, -2, -2, -2, -1, 0)(1, 1, 1, 2, 1, 1, 1)g_{44}
g_{-46}		-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 502(0, 0, 0, 0, 0, -1, 0)(0, 1, 1, 2, 2, 1, 1)g_{45}
g_{-6}		-\varepsilon_{4}-\varepsilon_{6}
-\varepsilon_{4}+\varepsilon_{5}
Module 512(-1, -1, -1, -2, -1, -1, -1)(1, 1, 2, 2, 2, 1, 0)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}
Module 522(-1, -1, -1, -2, -2, -1, 0)(1, 1, 2, 2, 1, 1, 1)g_{47}
g_{-43}		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 532(-1, -1, -2, -2, -1, -1, 0)(1, 1, 1, 2, 2, 1, 1)g_{48}
g_{-42}		-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 543(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 552(-1, -1, -1, -1, -1, -1, -1)(1, 1, 2, 3, 2, 1, 0)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}
Module 562(-1, -1, -1, -2, -1, -1, 0)(1, 1, 2, 2, 2, 1, 1)g_{51}
g_{-38}		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 574(-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 582(-1, 0, -1, -1, -1, -1, -1)(1, 2, 2, 3, 2, 1, 0)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}
Module 592(-1, -1, -1, -1, -1, -1, 0)(1, 1, 2, 3, 2, 1, 1)g_{54}
g_{-33}		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 604(-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 612(-1, 0, -1, -1, -1, -1, 0)(1, 2, 2, 3, 2, 1, 1)g_{56}
g_{-28}		-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 624(-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 634(-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 644(-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 654(-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 664(-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 674(-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 683(-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 691(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{2}0
Module 701(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{3}0
Module 711(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{4}0
Module 721(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{5}0
Module 731(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{7}0
Information about the subalgebra generation algorithm.
Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 42
Heirs rejected due to not being maximally dominant: 24
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 24
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
Parabolically induced by A^{1}_1
Potential Dynkin type extensions: 3A^{1}_1,