Type: \(\displaystyle A^{2}_1\) (Dynkin type computed to be: \(\displaystyle A^{2}_1\))
Simple basis: 1 vectors: (1, 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}: 0
simple basis centralizer: 0 vectors:
Number of k-submodules of g: 4
Module decomposition, fundamental coords over k: \(\displaystyle 3V_{2\omega_{1}}+V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 13(-1, -2)(1, 0)g_{1}
g_{-2}
g_{-4}		\varepsilon_{1}-\varepsilon_{2}
-\varepsilon_{2}
-\varepsilon_{1}-\varepsilon_{2}
Module 23(-1, -1)(1, 1)g_{3}
h_{2}+h_{1}
g_{-3}		\varepsilon_{1}
0
-\varepsilon_{1}
Module 33(-1, 0)(1, 2)g_{4}
g_{2}
g_{-1}		\varepsilon_{1}+\varepsilon_{2}
\varepsilon_{2}
-\varepsilon_{1}+\varepsilon_{2}
Module 41(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: 3
Heirs rejected due to not being maximally dominant: 0
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 0
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^{2}_2, B^{2}_2, 2A^{2}_1, A^{2}_1+A^{1}_1,