Type: \(\displaystyle A^{2}_1+A^{1}_1\) (Dynkin type computed to be: \(\displaystyle A^{2}_1+A^{1}_1\))
Simple basis: 2 vectors: (1, 1, 1), (0, 1, 2)
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, 0)
Number of k-submodules of g: 7
Module decomposition, fundamental coords over k: \(\displaystyle 2V_{2\omega_{1}+\omega_{2}}+V_{2\omega_{2}}+V_{2\omega_{1}}+3V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, -1, 0)(0, -1, 0)g_{-2}-\varepsilon_{2}+\varepsilon_{3}
Module 21(0, 1, 0)(0, 1, 0)g_{2}\varepsilon_{2}-\varepsilon_{3}
Module 33(-1, -1, -1)(1, 1, 1)g_{6}
h_{3}+h_{2}+h_{1}
g_{-6}		\varepsilon_{1}
0
-\varepsilon_{1}
Module 43(0, -1, -2)(0, 1, 2)g_{7}
2h_{3}+h_{2}
g_{-7}		\varepsilon_{2}+\varepsilon_{3}
0
-\varepsilon_{2}-\varepsilon_{3}
Module 56(-1, -2, -2)(1, 1, 2)g_{8}
g_{3}
g_{1}
g_{-4}
g_{-5}
g_{-9}		\varepsilon_{1}+\varepsilon_{3}
\varepsilon_{3}
\varepsilon_{1}-\varepsilon_{2}
-\varepsilon_{1}+\varepsilon_{3}
-\varepsilon_{2}
-\varepsilon_{1}-\varepsilon_{2}
Module 66(-1, -1, -2)(1, 2, 2)g_{9}
g_{5}
g_{4}
g_{-1}
g_{-3}
g_{-8}		\varepsilon_{1}+\varepsilon_{2}
\varepsilon_{2}
\varepsilon_{1}-\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{2}
-\varepsilon_{3}
-\varepsilon_{1}-\varepsilon_{3}
Module 71(0, 0, 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: 4
Heirs rejected due to not being maximally dominant: 1
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 1
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
Parabolically induced by A^{2}_1
Potential Dynkin type extensions: A^{2}_1+2A^{1}_1,