Type: \(\displaystyle A^{1}_1\) (Dynkin type computed to be: \(\displaystyle A^{1}_1\))
Simple basis: 1 vectors: (2, 2, 3, 4, 3, 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}_6
simple basis centralizer: 6 vectors: (0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1), (0, 0, 0, 1, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0)
Number of k-submodules of g: 99
Module decomposition, fundamental coords over k: \(\displaystyle V_{2\omega_{1}}+32V_{\omega_{1}}+66V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, -1, -1, -2, -2, -2, -1)(0, -1, -1, -2, -2, -2, -1)g_{-49}\varepsilon_{5}+\varepsilon_{6}
Module 21(0, -1, -1, -2, -2, -1, -1)(0, -1, -1, -2, -2, -1, -1)g_{-45}\varepsilon_{4}+\varepsilon_{6}
Module 31(0, -1, -1, -2, -1, -1, -1)(0, -1, -1, -2, -1, -1, -1)g_{-41}\varepsilon_{3}+\varepsilon_{6}
Module 41(0, -1, -1, -2, -2, -1, 0)(0, -1, -1, -2, -2, -1, 0)g_{-39}\varepsilon_{4}+\varepsilon_{5}
Module 51(0, -1, -1, -1, -1, -1, -1)(0, -1, -1, -1, -1, -1, -1)g_{-36}\varepsilon_{2}+\varepsilon_{6}
Module 61(0, -1, -1, -2, -1, -1, 0)(0, -1, -1, -2, -1, -1, 0)g_{-34}\varepsilon_{3}+\varepsilon_{5}
Module 71(0, 0, -1, -1, -1, -1, -1)(0, 0, -1, -1, -1, -1, -1)g_{-31}-\varepsilon_{1}+\varepsilon_{6}
Module 81(0, -1, 0, -1, -1, -1, -1)(0, -1, 0, -1, -1, -1, -1)g_{-30}\varepsilon_{1}+\varepsilon_{6}
Module 91(0, -1, -1, -1, -1, -1, 0)(0, -1, -1, -1, -1, -1, 0)g_{-29}\varepsilon_{2}+\varepsilon_{5}
Module 101(0, -1, -1, -2, -1, 0, 0)(0, -1, -1, -2, -1, 0, 0)g_{-27}\varepsilon_{3}+\varepsilon_{4}
Module 111(0, 0, 0, -1, -1, -1, -1)(0, 0, 0, -1, -1, -1, -1)g_{-25}-\varepsilon_{2}+\varepsilon_{6}
Module 121(0, 0, -1, -1, -1, -1, 0)(0, 0, -1, -1, -1, -1, 0)g_{-24}-\varepsilon_{1}+\varepsilon_{5}
Module 131(0, -1, 0, -1, -1, -1, 0)(0, -1, 0, -1, -1, -1, 0)g_{-23}\varepsilon_{1}+\varepsilon_{5}
Module 141(0, -1, -1, -1, -1, 0, 0)(0, -1, -1, -1, -1, 0, 0)g_{-22}\varepsilon_{2}+\varepsilon_{4}
Module 151(0, 0, 0, 0, -1, -1, -1)(0, 0, 0, 0, -1, -1, -1)g_{-19}-\varepsilon_{3}+\varepsilon_{6}
Module 161(0, 0, 0, -1, -1, -1, 0)(0, 0, 0, -1, -1, -1, 0)g_{-18}-\varepsilon_{2}+\varepsilon_{5}
Module 171(0, 0, -1, -1, -1, 0, 0)(0, 0, -1, -1, -1, 0, 0)g_{-17}-\varepsilon_{1}+\varepsilon_{4}
Module 181(0, -1, 0, -1, -1, 0, 0)(0, -1, 0, -1, -1, 0, 0)g_{-16}\varepsilon_{1}+\varepsilon_{4}
Module 191(0, -1, -1, -1, 0, 0, 0)(0, -1, -1, -1, 0, 0, 0)g_{-15}\varepsilon_{2}+\varepsilon_{3}
Module 201(0, 0, 0, 0, 0, -1, -1)(0, 0, 0, 0, 0, -1, -1)g_{-13}-\varepsilon_{4}+\varepsilon_{6}
Module 211(0, 0, 0, 0, -1, -1, 0)(0, 0, 0, 0, -1, -1, 0)g_{-12}-\varepsilon_{3}+\varepsilon_{5}
Module 221(0, 0, 0, -1, -1, 0, 0)(0, 0, 0, -1, -1, 0, 0)g_{-11}-\varepsilon_{2}+\varepsilon_{4}
Module 231(0, 0, -1, -1, 0, 0, 0)(0, 0, -1, -1, 0, 0, 0)g_{-10}-\varepsilon_{1}+\varepsilon_{3}
Module 241(0, -1, 0, -1, 0, 0, 0)(0, -1, 0, -1, 0, 0, 0)g_{-9}\varepsilon_{1}+\varepsilon_{3}
Module 251(0, 0, 0, 0, 0, 0, -1)(0, 0, 0, 0, 0, 0, -1)g_{-7}-\varepsilon_{5}+\varepsilon_{6}
Module 261(0, 0, 0, 0, 0, -1, 0)(0, 0, 0, 0, 0, -1, 0)g_{-6}-\varepsilon_{4}+\varepsilon_{5}
Module 271(0, 0, 0, 0, -1, 0, 0)(0, 0, 0, 0, -1, 0, 0)g_{-5}-\varepsilon_{3}+\varepsilon_{4}
Module 281(0, 0, 0, -1, 0, 0, 0)(0, 0, 0, -1, 0, 0, 0)g_{-4}-\varepsilon_{2}+\varepsilon_{3}
Module 291(0, 0, -1, 0, 0, 0, 0)(0, 0, -1, 0, 0, 0, 0)g_{-3}-\varepsilon_{1}+\varepsilon_{2}
Module 301(0, -1, 0, 0, 0, 0, 0)(0, -1, 0, 0, 0, 0, 0)g_{-2}\varepsilon_{1}+\varepsilon_{2}
Module 312(-1, -2, -3, -4, -3, -2, -1)(1, 0, 0, 0, 0, 0, 0)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}
Module 321(0, 1, 0, 0, 0, 0, 0)(0, 1, 0, 0, 0, 0, 0)g_{2}-\varepsilon_{1}-\varepsilon_{2}
Module 331(0, 0, 1, 0, 0, 0, 0)(0, 0, 1, 0, 0, 0, 0)g_{3}\varepsilon_{1}-\varepsilon_{2}
Module 341(0, 0, 0, 1, 0, 0, 0)(0, 0, 0, 1, 0, 0, 0)g_{4}\varepsilon_{2}-\varepsilon_{3}
Module 351(0, 0, 0, 0, 1, 0, 0)(0, 0, 0, 0, 1, 0, 0)g_{5}\varepsilon_{3}-\varepsilon_{4}
Module 361(0, 0, 0, 0, 0, 1, 0)(0, 0, 0, 0, 0, 1, 0)g_{6}\varepsilon_{4}-\varepsilon_{5}
Module 371(0, 0, 0, 0, 0, 0, 1)(0, 0, 0, 0, 0, 0, 1)g_{7}\varepsilon_{5}-\varepsilon_{6}
Module 382(-1, -2, -2, -4, -3, -2, -1)(1, 0, 1, 0, 0, 0, 0)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}
Module 391(0, 1, 0, 1, 0, 0, 0)(0, 1, 0, 1, 0, 0, 0)g_{9}-\varepsilon_{1}-\varepsilon_{3}
Module 401(0, 0, 1, 1, 0, 0, 0)(0, 0, 1, 1, 0, 0, 0)g_{10}\varepsilon_{1}-\varepsilon_{3}
Module 411(0, 0, 0, 1, 1, 0, 0)(0, 0, 0, 1, 1, 0, 0)g_{11}\varepsilon_{2}-\varepsilon_{4}
Module 421(0, 0, 0, 0, 1, 1, 0)(0, 0, 0, 0, 1, 1, 0)g_{12}\varepsilon_{3}-\varepsilon_{5}
Module 431(0, 0, 0, 0, 0, 1, 1)(0, 0, 0, 0, 0, 1, 1)g_{13}\varepsilon_{4}-\varepsilon_{6}
Module 442(-1, -2, -2, -3, -3, -2, -1)(1, 0, 1, 1, 0, 0, 0)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}
Module 451(0, 1, 1, 1, 0, 0, 0)(0, 1, 1, 1, 0, 0, 0)g_{15}-\varepsilon_{2}-\varepsilon_{3}
Module 461(0, 1, 0, 1, 1, 0, 0)(0, 1, 0, 1, 1, 0, 0)g_{16}-\varepsilon_{1}-\varepsilon_{4}
Module 471(0, 0, 1, 1, 1, 0, 0)(0, 0, 1, 1, 1, 0, 0)g_{17}\varepsilon_{1}-\varepsilon_{4}
Module 481(0, 0, 0, 1, 1, 1, 0)(0, 0, 0, 1, 1, 1, 0)g_{18}\varepsilon_{2}-\varepsilon_{5}
Module 491(0, 0, 0, 0, 1, 1, 1)(0, 0, 0, 0, 1, 1, 1)g_{19}\varepsilon_{3}-\varepsilon_{6}
Module 502(-1, -1, -2, -3, -3, -2, -1)(1, 1, 1, 1, 0, 0, 0)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}
Module 512(-1, -2, -2, -3, -2, -2, -1)(1, 0, 1, 1, 1, 0, 0)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}
Module 521(0, 1, 1, 1, 1, 0, 0)(0, 1, 1, 1, 1, 0, 0)g_{22}-\varepsilon_{2}-\varepsilon_{4}
Module 531(0, 1, 0, 1, 1, 1, 0)(0, 1, 0, 1, 1, 1, 0)g_{23}-\varepsilon_{1}-\varepsilon_{5}
Module 541(0, 0, 1, 1, 1, 1, 0)(0, 0, 1, 1, 1, 1, 0)g_{24}\varepsilon_{1}-\varepsilon_{5}
Module 551(0, 0, 0, 1, 1, 1, 1)(0, 0, 0, 1, 1, 1, 1)g_{25}\varepsilon_{2}-\varepsilon_{6}
Module 562(-1, -1, -2, -3, -2, -2, -1)(1, 1, 1, 1, 1, 0, 0)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}
Module 571(0, 1, 1, 2, 1, 0, 0)(0, 1, 1, 2, 1, 0, 0)g_{27}-\varepsilon_{3}-\varepsilon_{4}
Module 582(-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 591(0, 1, 1, 1, 1, 1, 0)(0, 1, 1, 1, 1, 1, 0)g_{29}-\varepsilon_{2}-\varepsilon_{5}
Module 601(0, 1, 0, 1, 1, 1, 1)(0, 1, 0, 1, 1, 1, 1)g_{30}-\varepsilon_{1}-\varepsilon_{6}
Module 611(0, 0, 1, 1, 1, 1, 1)(0, 0, 1, 1, 1, 1, 1)g_{31}\varepsilon_{1}-\varepsilon_{6}
Module 622(-1, -1, -2, -2, -2, -2, -1)(1, 1, 1, 2, 1, 0, 0)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}
Module 632(-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 641(0, 1, 1, 2, 1, 1, 0)(0, 1, 1, 2, 1, 1, 0)g_{34}-\varepsilon_{3}-\varepsilon_{5}
Module 652(-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 661(0, 1, 1, 1, 1, 1, 1)(0, 1, 1, 1, 1, 1, 1)g_{36}-\varepsilon_{2}-\varepsilon_{6}
Module 672(-1, -1, -1, -2, -2, -2, -1)(1, 1, 2, 2, 1, 0, 0)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}
Module 682(-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 691(0, 1, 1, 2, 2, 1, 0)(0, 1, 1, 2, 2, 1, 0)g_{39}-\varepsilon_{4}-\varepsilon_{5}
Module 702(-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 711(0, 1, 1, 2, 1, 1, 1)(0, 1, 1, 2, 1, 1, 1)g_{41}-\varepsilon_{3}-\varepsilon_{6}
Module 722(-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 732(-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 742(-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 751(0, 1, 1, 2, 2, 1, 1)(0, 1, 1, 2, 2, 1, 1)g_{45}-\varepsilon_{4}-\varepsilon_{6}
Module 762(-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 772(-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 782(-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 791(0, 1, 1, 2, 2, 2, 1)(0, 1, 1, 2, 2, 2, 1)g_{49}-\varepsilon_{5}-\varepsilon_{6}
Module 802(-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 812(-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 822(-1, -1, -2, -2, -1, 0, 0)(1, 1, 1, 2, 2, 2, 1)g_{52}
g_{-37}		-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 832(-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 842(-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 852(-1, -1, -1, -2, -1, 0, 0)(1, 1, 2, 2, 2, 2, 1)g_{55}
g_{-32}		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 862(-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 872(-1, -1, -1, -1, -1, 0, 0)(1, 1, 2, 3, 2, 2, 1)g_{57}
g_{-26}		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 882(-1, 0, -1, -1, -1, 0, 0)(1, 2, 2, 3, 2, 2, 1)g_{58}
g_{-21}		-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 892(-1, -1, -1, -1, 0, 0, 0)(1, 1, 2, 3, 3, 2, 1)g_{59}
g_{-20}		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 902(-1, 0, -1, -1, 0, 0, 0)(1, 2, 2, 3, 3, 2, 1)g_{60}
g_{-14}		-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 912(-1, 0, -1, 0, 0, 0, 0)(1, 2, 2, 4, 3, 2, 1)g_{61}
g_{-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 922(-1, 0, 0, 0, 0, 0, 0)(1, 2, 3, 4, 3, 2, 1)g_{62}
g_{-1}		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 933(-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 941(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{2}0
Module 951(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{3}0
Module 961(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{4}0
Module 971(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{5}0
Module 981(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{6}0
Module 991(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: 1
Heirs rejected due to not being maximally dominant: 90
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 90
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
Parabolically induced by 0
Potential Dynkin type extensions: A^{1}_2, 2A^{1}_1,