Type: \(\displaystyle 0\) (Dynkin type computed to be: \(\displaystyle 0\))
Simple basis: 0 vectors:
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}_7
simple basis centralizer: 7 vectors: (1, 0, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1), (0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0)
Number of k-submodules of g: 63
Module decomposition, fundamental coords over k: \(\displaystyle 63V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(-1, -1, -1, -1, -1, -1, -1)(-1, -1, -1, -1, -1, -1, -1)g_{-28}-\varepsilon_{1}+\varepsilon_{8}
Module 21(0, -1, -1, -1, -1, -1, -1)(0, -1, -1, -1, -1, -1, -1)g_{-27}-\varepsilon_{2}+\varepsilon_{8}
Module 31(-1, -1, -1, -1, -1, -1, 0)(-1, -1, -1, -1, -1, -1, 0)g_{-26}-\varepsilon_{1}+\varepsilon_{7}
Module 41(0, 0, -1, -1, -1, -1, -1)(0, 0, -1, -1, -1, -1, -1)g_{-25}-\varepsilon_{3}+\varepsilon_{8}
Module 51(0, -1, -1, -1, -1, -1, 0)(0, -1, -1, -1, -1, -1, 0)g_{-24}-\varepsilon_{2}+\varepsilon_{7}
Module 61(-1, -1, -1, -1, -1, 0, 0)(-1, -1, -1, -1, -1, 0, 0)g_{-23}-\varepsilon_{1}+\varepsilon_{6}
Module 71(0, 0, 0, -1, -1, -1, -1)(0, 0, 0, -1, -1, -1, -1)g_{-22}-\varepsilon_{4}+\varepsilon_{8}
Module 81(0, 0, -1, -1, -1, -1, 0)(0, 0, -1, -1, -1, -1, 0)g_{-21}-\varepsilon_{3}+\varepsilon_{7}
Module 91(0, -1, -1, -1, -1, 0, 0)(0, -1, -1, -1, -1, 0, 0)g_{-20}-\varepsilon_{2}+\varepsilon_{6}
Module 101(-1, -1, -1, -1, 0, 0, 0)(-1, -1, -1, -1, 0, 0, 0)g_{-19}-\varepsilon_{1}+\varepsilon_{5}
Module 111(0, 0, 0, 0, -1, -1, -1)(0, 0, 0, 0, -1, -1, -1)g_{-18}-\varepsilon_{5}+\varepsilon_{8}
Module 121(0, 0, 0, -1, -1, -1, 0)(0, 0, 0, -1, -1, -1, 0)g_{-17}-\varepsilon_{4}+\varepsilon_{7}
Module 131(0, 0, -1, -1, -1, 0, 0)(0, 0, -1, -1, -1, 0, 0)g_{-16}-\varepsilon_{3}+\varepsilon_{6}
Module 141(0, -1, -1, -1, 0, 0, 0)(0, -1, -1, -1, 0, 0, 0)g_{-15}-\varepsilon_{2}+\varepsilon_{5}
Module 151(-1, -1, -1, 0, 0, 0, 0)(-1, -1, -1, 0, 0, 0, 0)g_{-14}-\varepsilon_{1}+\varepsilon_{4}
Module 161(0, 0, 0, 0, 0, -1, -1)(0, 0, 0, 0, 0, -1, -1)g_{-13}-\varepsilon_{6}+\varepsilon_{8}
Module 171(0, 0, 0, 0, -1, -1, 0)(0, 0, 0, 0, -1, -1, 0)g_{-12}-\varepsilon_{5}+\varepsilon_{7}
Module 181(0, 0, 0, -1, -1, 0, 0)(0, 0, 0, -1, -1, 0, 0)g_{-11}-\varepsilon_{4}+\varepsilon_{6}
Module 191(0, 0, -1, -1, 0, 0, 0)(0, 0, -1, -1, 0, 0, 0)g_{-10}-\varepsilon_{3}+\varepsilon_{5}
Module 201(0, -1, -1, 0, 0, 0, 0)(0, -1, -1, 0, 0, 0, 0)g_{-9}-\varepsilon_{2}+\varepsilon_{4}
Module 211(-1, -1, 0, 0, 0, 0, 0)(-1, -1, 0, 0, 0, 0, 0)g_{-8}-\varepsilon_{1}+\varepsilon_{3}
Module 221(0, 0, 0, 0, 0, 0, -1)(0, 0, 0, 0, 0, 0, -1)g_{-7}-\varepsilon_{7}+\varepsilon_{8}
Module 231(0, 0, 0, 0, 0, -1, 0)(0, 0, 0, 0, 0, -1, 0)g_{-6}-\varepsilon_{6}+\varepsilon_{7}
Module 241(0, 0, 0, 0, -1, 0, 0)(0, 0, 0, 0, -1, 0, 0)g_{-5}-\varepsilon_{5}+\varepsilon_{6}
Module 251(0, 0, 0, -1, 0, 0, 0)(0, 0, 0, -1, 0, 0, 0)g_{-4}-\varepsilon_{4}+\varepsilon_{5}
Module 261(0, 0, -1, 0, 0, 0, 0)(0, 0, -1, 0, 0, 0, 0)g_{-3}-\varepsilon_{3}+\varepsilon_{4}
Module 271(0, -1, 0, 0, 0, 0, 0)(0, -1, 0, 0, 0, 0, 0)g_{-2}-\varepsilon_{2}+\varepsilon_{3}
Module 281(-1, 0, 0, 0, 0, 0, 0)(-1, 0, 0, 0, 0, 0, 0)g_{-1}-\varepsilon_{1}+\varepsilon_{2}
Module 291(1, 0, 0, 0, 0, 0, 0)(1, 0, 0, 0, 0, 0, 0)g_{1}\varepsilon_{1}-\varepsilon_{2}
Module 301(0, 1, 0, 0, 0, 0, 0)(0, 1, 0, 0, 0, 0, 0)g_{2}\varepsilon_{2}-\varepsilon_{3}
Module 311(0, 0, 1, 0, 0, 0, 0)(0, 0, 1, 0, 0, 0, 0)g_{3}\varepsilon_{3}-\varepsilon_{4}
Module 321(0, 0, 0, 1, 0, 0, 0)(0, 0, 0, 1, 0, 0, 0)g_{4}\varepsilon_{4}-\varepsilon_{5}
Module 331(0, 0, 0, 0, 1, 0, 0)(0, 0, 0, 0, 1, 0, 0)g_{5}\varepsilon_{5}-\varepsilon_{6}
Module 341(0, 0, 0, 0, 0, 1, 0)(0, 0, 0, 0, 0, 1, 0)g_{6}\varepsilon_{6}-\varepsilon_{7}
Module 351(0, 0, 0, 0, 0, 0, 1)(0, 0, 0, 0, 0, 0, 1)g_{7}\varepsilon_{7}-\varepsilon_{8}
Module 361(1, 1, 0, 0, 0, 0, 0)(1, 1, 0, 0, 0, 0, 0)g_{8}\varepsilon_{1}-\varepsilon_{3}
Module 371(0, 1, 1, 0, 0, 0, 0)(0, 1, 1, 0, 0, 0, 0)g_{9}\varepsilon_{2}-\varepsilon_{4}
Module 381(0, 0, 1, 1, 0, 0, 0)(0, 0, 1, 1, 0, 0, 0)g_{10}\varepsilon_{3}-\varepsilon_{5}
Module 391(0, 0, 0, 1, 1, 0, 0)(0, 0, 0, 1, 1, 0, 0)g_{11}\varepsilon_{4}-\varepsilon_{6}
Module 401(0, 0, 0, 0, 1, 1, 0)(0, 0, 0, 0, 1, 1, 0)g_{12}\varepsilon_{5}-\varepsilon_{7}
Module 411(0, 0, 0, 0, 0, 1, 1)(0, 0, 0, 0, 0, 1, 1)g_{13}\varepsilon_{6}-\varepsilon_{8}
Module 421(1, 1, 1, 0, 0, 0, 0)(1, 1, 1, 0, 0, 0, 0)g_{14}\varepsilon_{1}-\varepsilon_{4}
Module 431(0, 1, 1, 1, 0, 0, 0)(0, 1, 1, 1, 0, 0, 0)g_{15}\varepsilon_{2}-\varepsilon_{5}
Module 441(0, 0, 1, 1, 1, 0, 0)(0, 0, 1, 1, 1, 0, 0)g_{16}\varepsilon_{3}-\varepsilon_{6}
Module 451(0, 0, 0, 1, 1, 1, 0)(0, 0, 0, 1, 1, 1, 0)g_{17}\varepsilon_{4}-\varepsilon_{7}
Module 461(0, 0, 0, 0, 1, 1, 1)(0, 0, 0, 0, 1, 1, 1)g_{18}\varepsilon_{5}-\varepsilon_{8}
Module 471(1, 1, 1, 1, 0, 0, 0)(1, 1, 1, 1, 0, 0, 0)g_{19}\varepsilon_{1}-\varepsilon_{5}
Module 481(0, 1, 1, 1, 1, 0, 0)(0, 1, 1, 1, 1, 0, 0)g_{20}\varepsilon_{2}-\varepsilon_{6}
Module 491(0, 0, 1, 1, 1, 1, 0)(0, 0, 1, 1, 1, 1, 0)g_{21}\varepsilon_{3}-\varepsilon_{7}
Module 501(0, 0, 0, 1, 1, 1, 1)(0, 0, 0, 1, 1, 1, 1)g_{22}\varepsilon_{4}-\varepsilon_{8}
Module 511(1, 1, 1, 1, 1, 0, 0)(1, 1, 1, 1, 1, 0, 0)g_{23}\varepsilon_{1}-\varepsilon_{6}
Module 521(0, 1, 1, 1, 1, 1, 0)(0, 1, 1, 1, 1, 1, 0)g_{24}\varepsilon_{2}-\varepsilon_{7}
Module 531(0, 0, 1, 1, 1, 1, 1)(0, 0, 1, 1, 1, 1, 1)g_{25}\varepsilon_{3}-\varepsilon_{8}
Module 541(1, 1, 1, 1, 1, 1, 0)(1, 1, 1, 1, 1, 1, 0)g_{26}\varepsilon_{1}-\varepsilon_{7}
Module 551(0, 1, 1, 1, 1, 1, 1)(0, 1, 1, 1, 1, 1, 1)g_{27}\varepsilon_{2}-\varepsilon_{8}
Module 561(1, 1, 1, 1, 1, 1, 1)(1, 1, 1, 1, 1, 1, 1)g_{28}\varepsilon_{1}-\varepsilon_{8}
Module 571(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{1}0
Module 581(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{2}0
Module 591(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{3}0
Module 601(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{4}0
Module 611(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{5}0
Module 621(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{6}0
Module 631(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: 0
Heirs rejected due to not being maximally dominant: 55
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 55
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
This subalgebra is not parabolically induced by anyone
Potential Dynkin type extensions: A^{1}_1,