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}: F^{1}_4
simple basis centralizer: 4 vectors: (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1)
Number of k-submodules of g: 52
Module decomposition, fundamental coords over k: \(\displaystyle 52V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(-2, -3, -4, -2)(-2, -3, -4, -2)g_{-24}-\varepsilon_{1}+\varepsilon_{4}
Module 21(-1, -3, -4, -2)(-1, -3, -4, -2)g_{-23}-\varepsilon_{2}+\varepsilon_{4}
Module 31(-1, -2, -4, -2)(-1, -2, -4, -2)g_{-22}-\varepsilon_{3}+\varepsilon_{4}
Module 41(-1, -2, -3, -2)(-1, -2, -3, -2)g_{-21}\varepsilon_{4}
Module 51(-1, -2, -2, -2)(-1, -2, -2, -2)g_{-20}\varepsilon_{3}+\varepsilon_{4}
Module 61(-1, -2, -3, -1)(-1, -2, -3, -1)g_{-19}-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 71(-1, -1, -2, -2)(-1, -1, -2, -2)g_{-18}\varepsilon_{2}+\varepsilon_{4}
Module 81(-1, -2, -2, -1)(-1, -2, -2, -1)g_{-17}-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 91(0, -1, -2, -2)(0, -1, -2, -2)g_{-16}\varepsilon_{1}+\varepsilon_{4}
Module 101(-1, -1, -2, -1)(-1, -1, -2, -1)g_{-15}-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 111(-1, -2, -2, 0)(-1, -2, -2, 0)g_{-14}-\varepsilon_{1}-\varepsilon_{2}
Module 121(0, -1, -2, -1)(0, -1, -2, -1)g_{-13}1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 131(-1, -1, -1, -1)(-1, -1, -1, -1)g_{-12}-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 141(-1, -1, -2, 0)(-1, -1, -2, 0)g_{-11}-\varepsilon_{1}-\varepsilon_{3}
Module 151(0, -1, -1, -1)(0, -1, -1, -1)g_{-10}1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 161(0, -1, -2, 0)(0, -1, -2, 0)g_{-9}-\varepsilon_{2}-\varepsilon_{3}
Module 171(-1, -1, -1, 0)(-1, -1, -1, 0)g_{-8}-\varepsilon_{1}
Module 181(0, 0, -1, -1)(0, 0, -1, -1)g_{-7}1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 191(0, -1, -1, 0)(0, -1, -1, 0)g_{-6}-\varepsilon_{2}
Module 201(-1, -1, 0, 0)(-1, -1, 0, 0)g_{-5}-\varepsilon_{1}+\varepsilon_{3}
Module 211(0, 0, 0, -1)(0, 0, 0, -1)g_{-4}1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}
Module 221(0, 0, -1, 0)(0, 0, -1, 0)g_{-3}-\varepsilon_{3}
Module 231(0, -1, 0, 0)(0, -1, 0, 0)g_{-2}-\varepsilon_{2}+\varepsilon_{3}
Module 241(-1, 0, 0, 0)(-1, 0, 0, 0)g_{-1}-\varepsilon_{1}+\varepsilon_{2}
Module 251(1, 0, 0, 0)(1, 0, 0, 0)g_{1}\varepsilon_{1}-\varepsilon_{2}
Module 261(0, 1, 0, 0)(0, 1, 0, 0)g_{2}\varepsilon_{2}-\varepsilon_{3}
Module 271(0, 0, 1, 0)(0, 0, 1, 0)g_{3}\varepsilon_{3}
Module 281(0, 0, 0, 1)(0, 0, 0, 1)g_{4}-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 291(1, 1, 0, 0)(1, 1, 0, 0)g_{5}\varepsilon_{1}-\varepsilon_{3}
Module 301(0, 1, 1, 0)(0, 1, 1, 0)g_{6}\varepsilon_{2}
Module 311(0, 0, 1, 1)(0, 0, 1, 1)g_{7}-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 321(1, 1, 1, 0)(1, 1, 1, 0)g_{8}\varepsilon_{1}
Module 331(0, 1, 2, 0)(0, 1, 2, 0)g_{9}\varepsilon_{2}+\varepsilon_{3}
Module 341(0, 1, 1, 1)(0, 1, 1, 1)g_{10}-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 351(1, 1, 2, 0)(1, 1, 2, 0)g_{11}\varepsilon_{1}+\varepsilon_{3}
Module 361(1, 1, 1, 1)(1, 1, 1, 1)g_{12}1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 371(0, 1, 2, 1)(0, 1, 2, 1)g_{13}-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 381(1, 2, 2, 0)(1, 2, 2, 0)g_{14}\varepsilon_{1}+\varepsilon_{2}
Module 391(1, 1, 2, 1)(1, 1, 2, 1)g_{15}1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 401(0, 1, 2, 2)(0, 1, 2, 2)g_{16}-\varepsilon_{1}-\varepsilon_{4}
Module 411(1, 2, 2, 1)(1, 2, 2, 1)g_{17}1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 421(1, 1, 2, 2)(1, 1, 2, 2)g_{18}-\varepsilon_{2}-\varepsilon_{4}
Module 431(1, 2, 3, 1)(1, 2, 3, 1)g_{19}1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}
Module 441(1, 2, 2, 2)(1, 2, 2, 2)g_{20}-\varepsilon_{3}-\varepsilon_{4}
Module 451(1, 2, 3, 2)(1, 2, 3, 2)g_{21}-\varepsilon_{4}
Module 461(1, 2, 4, 2)(1, 2, 4, 2)g_{22}\varepsilon_{3}-\varepsilon_{4}
Module 471(1, 3, 4, 2)(1, 3, 4, 2)g_{23}\varepsilon_{2}-\varepsilon_{4}
Module 481(2, 3, 4, 2)(2, 3, 4, 2)g_{24}\varepsilon_{1}-\varepsilon_{4}
Module 491(0, 0, 0, 0)(0, 0, 0, 0)h_{1}0
Module 501(0, 0, 0, 0)(0, 0, 0, 0)h_{2}0
Module 511(0, 0, 0, 0)(0, 0, 0, 0)h_{3}0
Module 521(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: 0
Heirs rejected due to not being maximally dominant: 46
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 46
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, A^{2}_1,