Type: \(\displaystyle G^{1}_2\) (Dynkin type computed to be: \(\displaystyle G^{1}_2\))
Simple basis: 2 vectors: (2, 1), (-3, -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: 1
Module decomposition, fundamental coords over k: \(\displaystyle V_{\omega_{2}}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 114(0, -1)(0, 1)g_{2}
g_{6}
g_{3}
g_{-1}
g_{-5}
g_{4}
-h_{2}-3h_{1}
h_{2}+2h_{1}
g_{-4}
g_{5}
g_{1}
g_{-3}
g_{-6}
g_{-2}		-2\varepsilon_{1}+\varepsilon_{2}+\varepsilon_{3}
-\varepsilon_{1}-\varepsilon_{2}+2\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{2}
-\varepsilon_{1}+2\varepsilon_{2}-\varepsilon_{3}
-\varepsilon_{2}+\varepsilon_{3}
0
0
\varepsilon_{2}-\varepsilon_{3}
\varepsilon_{1}-2\varepsilon_{2}+\varepsilon_{3}
\varepsilon_{1}-\varepsilon_{2}
\varepsilon_{1}-\varepsilon_{3}
\varepsilon_{1}+\varepsilon_{2}-2\varepsilon_{3}
2\varepsilon_{1}-\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: 1
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^{3}_1
Potential Dynkin type extensions: