Type: \(\displaystyle A^{3}_1\) (Dynkin type computed to be: \(\displaystyle A^{3}_1\))
Simple basis: 1 vectors: (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}: A^{1}_1
simple basis centralizer: 1 vectors: (0, 1)
Number of k-submodules of g: 6
Module decomposition, fundamental coords over k: \(\displaystyle 2V_{3\omega_{1}}+V_{2\omega_{1}}+3V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, -1)(0, -1)g_{-2}2\varepsilon_{1}-\varepsilon_{2}-\varepsilon_{3}
Module 21(0, 1)(0, 1)g_{2}-2\varepsilon_{1}+\varepsilon_{2}+\varepsilon_{3}
Module 33(-2, -1)(2, 1)g_{4}
h_{2}+2h_{1}
g_{-4}		-\varepsilon_{2}+\varepsilon_{3}
0
\varepsilon_{2}-\varepsilon_{3}
Module 44(-3, -2)(3, 1)g_{5}
g_{1}
g_{-3}
g_{-6}		\varepsilon_{1}-2\varepsilon_{2}+\varepsilon_{3}
\varepsilon_{1}-\varepsilon_{2}
\varepsilon_{1}-\varepsilon_{3}
\varepsilon_{1}+\varepsilon_{2}-2\varepsilon_{3}
Module 54(-3, -1)(3, 2)g_{6}
g_{3}
g_{-1}
g_{-5}		-\varepsilon_{1}-\varepsilon_{2}+2\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{2}
-\varepsilon_{1}+2\varepsilon_{2}-\varepsilon_{3}
Module 61(0, 0)(0, 0)h_{2}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: 2
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 2
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^{3}_2, A^{3}_1+A^{1}_1, G^{1}_2, 2A^{3}_1,