Type: \(\displaystyle A^{1}_3\) (Dynkin type computed to be: \(\displaystyle A^{1}_3\))
Simple basis: 3 vectors: (1, 2, 2), (0, -1, 0), (-1, 0, 0)
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: 2
Module decomposition, fundamental coords over k: \(\displaystyle V_{\omega_{1}+\omega_{3}}+V_{\omega_{2}}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 16(0, 0, -1)(0, 0, 1)g_{3}
g_{5}
g_{-6}
g_{6}
g_{-5}
g_{-3}		\varepsilon_{3}
\varepsilon_{2}
-\varepsilon_{1}
\varepsilon_{1}
-\varepsilon_{2}
-\varepsilon_{3}
Module 215(0, -1, -2)(0, 1, 2)g_{7}
g_{-4}
g_{8}
g_{-1}
g_{-2}
g_{9}
-h_{1}
-h_{2}
2h_{3}+2h_{2}+h_{1}
g_{-9}
g_{2}
g_{1}
g_{-8}
g_{4}
g_{-7}		\varepsilon_{2}+\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{3}
\varepsilon_{1}+\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{2}
-\varepsilon_{2}+\varepsilon_{3}
\varepsilon_{1}+\varepsilon_{2}
0
0
0
-\varepsilon_{1}-\varepsilon_{2}
\varepsilon_{2}-\varepsilon_{3}
\varepsilon_{1}-\varepsilon_{2}
-\varepsilon_{1}-\varepsilon_{3}
\varepsilon_{1}-\varepsilon_{3}
-\varepsilon_{2}-\varepsilon_{3}
Information about the subalgebra generation algorithm.
Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 2
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 A^{1}_2
Potential Dynkin type extensions: