Type: \(\displaystyle 2A^{2}_1\) (Dynkin type computed to be: \(\displaystyle 2A^{2}_1\))
Simple basis: 2 vectors: (1, 2, 2, 2, 1), (0, 0, 1, 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, 0, 0, 0, 1)
Number of k-submodules of g: 23
Module decomposition, fundamental coords over k: \(\displaystyle 3V_{2\omega_{2}}+4V_{\omega_{1}+\omega_{2}}+3V_{2\omega_{1}}+4V_{\omega_{2}}+4V_{\omega_{1}}+5V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, 0, 0, 0, -1)(0, 0, 0, 0, -1)g_{-5}-2\varepsilon_{5}
Module 22(0, 0, -1, -1, -1)(0, 0, 0, 1, 0)g_{4}
g_{-12}		\varepsilon_{4}-\varepsilon_{5}
-\varepsilon_{3}-\varepsilon_{5}
Module 31(0, 0, 0, 0, 1)(0, 0, 0, 0, 1)g_{5}2\varepsilon_{5}
Module 42(0, 0, 0, -1, -1)(0, 0, 1, 1, 0)g_{8}
g_{-9}		\varepsilon_{3}-\varepsilon_{5}
-\varepsilon_{4}-\varepsilon_{5}
Module 52(0, 0, -1, -1, 0)(0, 0, 0, 1, 1)g_{9}
g_{-8}		\varepsilon_{4}+\varepsilon_{5}
-\varepsilon_{3}+\varepsilon_{5}
Module 62(-1, -1, -1, -1, -1)(0, 1, 1, 1, 0)g_{11}
g_{-17}		\varepsilon_{2}-\varepsilon_{5}
-\varepsilon_{1}-\varepsilon_{5}
Module 72(0, 0, 0, -1, 0)(0, 0, 1, 1, 1)g_{12}
g_{-4}		\varepsilon_{3}+\varepsilon_{5}
-\varepsilon_{4}+\varepsilon_{5}
Module 83(0, 0, -2, -2, -1)(0, 0, 0, 2, 1)g_{13}
g_{-3}
g_{-19}		2\varepsilon_{4}
-\varepsilon_{3}+\varepsilon_{4}
-2\varepsilon_{3}
Module 92(0, -1, -1, -1, -1)(1, 1, 1, 1, 0)g_{14}
g_{-15}		\varepsilon_{1}-\varepsilon_{5}
-\varepsilon_{2}-\varepsilon_{5}
Module 102(-1, -1, -1, -1, 0)(0, 1, 1, 1, 1)g_{15}
g_{-14}		\varepsilon_{2}+\varepsilon_{5}
-\varepsilon_{1}+\varepsilon_{5}
Module 113(0, 0, -1, -2, -1)(0, 0, 1, 2, 1)g_{16}
h_{5}+2h_{4}+h_{3}
g_{-16}		\varepsilon_{3}+\varepsilon_{4}
0
-\varepsilon_{3}-\varepsilon_{4}
Module 122(0, -1, -1, -1, 0)(1, 1, 1, 1, 1)g_{17}
g_{-11}		\varepsilon_{1}+\varepsilon_{5}
-\varepsilon_{2}+\varepsilon_{5}
Module 134(-1, -1, -2, -2, -1)(0, 1, 1, 2, 1)g_{18}
g_{-10}
g_{2}
g_{-22}		\varepsilon_{2}+\varepsilon_{4}
-\varepsilon_{1}+\varepsilon_{4}
\varepsilon_{2}-\varepsilon_{3}
-\varepsilon_{1}-\varepsilon_{3}
Module 143(0, 0, 0, -2, -1)(0, 0, 2, 2, 1)g_{19}
g_{3}
g_{-13}		2\varepsilon_{3}
\varepsilon_{3}-\varepsilon_{4}
-2\varepsilon_{4}
Module 154(0, -1, -2, -2, -1)(1, 1, 1, 2, 1)g_{20}
g_{-7}
g_{6}
g_{-21}		\varepsilon_{1}+\varepsilon_{4}
-\varepsilon_{2}+\varepsilon_{4}
\varepsilon_{1}-\varepsilon_{3}
-\varepsilon_{2}-\varepsilon_{3}
Module 164(-1, -1, -1, -2, -1)(0, 1, 2, 2, 1)g_{21}
g_{-6}
g_{7}
g_{-20}		\varepsilon_{2}+\varepsilon_{3}
-\varepsilon_{1}+\varepsilon_{3}
\varepsilon_{2}-\varepsilon_{4}
-\varepsilon_{1}-\varepsilon_{4}
Module 174(0, -1, -1, -2, -1)(1, 1, 2, 2, 1)g_{22}
g_{-2}
g_{10}
g_{-18}		\varepsilon_{1}+\varepsilon_{3}
-\varepsilon_{2}+\varepsilon_{3}
\varepsilon_{1}-\varepsilon_{4}
-\varepsilon_{2}-\varepsilon_{4}
Module 183(-2, -2, -2, -2, -1)(0, 2, 2, 2, 1)g_{23}
g_{-1}
g_{-25}		2\varepsilon_{2}
-\varepsilon_{1}+\varepsilon_{2}
-2\varepsilon_{1}
Module 193(-1, -2, -2, -2, -1)(1, 2, 2, 2, 1)g_{24}
h_{5}+2h_{4}+2h_{3}+2h_{2}+h_{1}
g_{-24}		\varepsilon_{1}+\varepsilon_{2}
0
-\varepsilon_{1}-\varepsilon_{2}
Module 203(0, -2, -2, -2, -1)(2, 2, 2, 2, 1)g_{25}
g_{1}
g_{-23}		2\varepsilon_{1}
\varepsilon_{1}-\varepsilon_{2}
-2\varepsilon_{2}
Module 211(0, 0, 0, 0, 0)(0, 0, 0, 0, 0)h_{1}0
Module 221(0, 0, 0, 0, 0)(0, 0, 0, 0, 0)h_{3}0
Module 231(0, 0, 0, 0, 0)(0, 0, 0, 0, 0)h_{5}0
Information about the subalgebra generation algorithm.
Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 18
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: 3A^{2}_1, 2A^{2}_1+A^{1}_1,