Type: \(\displaystyle A^{1}_2\) (Dynkin type computed to be: \(\displaystyle A^{1}_2\))
Simple basis: 2 vectors: (2, 2, 3, 4, 3, 2, 1), (-1, 0, 0, 0, 0, 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}: A^{1}_5
simple basis centralizer: 5 vectors: (0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 0, 0, 1), (0, 0, 0, 1, 0, 0, 0), (0, 0, 0, 0, 0, 1, 0), (0, 0, 0, 0, 1, 0, 0)
Number of k-submodules of g: 66
Module decomposition, fundamental coords over k: \(\displaystyle V_{\omega_{1}+\omega_{2}}+15V_{\omega_{2}}+15V_{\omega_{1}}+35V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(0, -1, 0, -1, -1, -1, -1)(0, -1, 0, -1, -1, -1, -1)g_{-30}\varepsilon_{1}+\varepsilon_{6}
Module 21(0, 0, 0, -1, -1, -1, -1)(0, 0, 0, -1, -1, -1, -1)g_{-25}-\varepsilon_{2}+\varepsilon_{6}
Module 31(0, -1, 0, -1, -1, -1, 0)(0, -1, 0, -1, -1, -1, 0)g_{-23}\varepsilon_{1}+\varepsilon_{5}
Module 41(0, 0, 0, 0, -1, -1, -1)(0, 0, 0, 0, -1, -1, -1)g_{-19}-\varepsilon_{3}+\varepsilon_{6}
Module 51(0, 0, 0, -1, -1, -1, 0)(0, 0, 0, -1, -1, -1, 0)g_{-18}-\varepsilon_{2}+\varepsilon_{5}
Module 61(0, -1, 0, -1, -1, 0, 0)(0, -1, 0, -1, -1, 0, 0)g_{-16}\varepsilon_{1}+\varepsilon_{4}
Module 71(0, 0, 0, 0, 0, -1, -1)(0, 0, 0, 0, 0, -1, -1)g_{-13}-\varepsilon_{4}+\varepsilon_{6}
Module 81(0, 0, 0, 0, -1, -1, 0)(0, 0, 0, 0, -1, -1, 0)g_{-12}-\varepsilon_{3}+\varepsilon_{5}
Module 91(0, 0, 0, -1, -1, 0, 0)(0, 0, 0, -1, -1, 0, 0)g_{-11}-\varepsilon_{2}+\varepsilon_{4}
Module 101(0, -1, 0, -1, 0, 0, 0)(0, -1, 0, -1, 0, 0, 0)g_{-9}\varepsilon_{1}+\varepsilon_{3}
Module 111(0, 0, 0, 0, 0, 0, -1)(0, 0, 0, 0, 0, 0, -1)g_{-7}-\varepsilon_{5}+\varepsilon_{6}
Module 121(0, 0, 0, 0, 0, -1, 0)(0, 0, 0, 0, 0, -1, 0)g_{-6}-\varepsilon_{4}+\varepsilon_{5}
Module 131(0, 0, 0, 0, -1, 0, 0)(0, 0, 0, 0, -1, 0, 0)g_{-5}-\varepsilon_{3}+\varepsilon_{4}
Module 141(0, 0, 0, -1, 0, 0, 0)(0, 0, 0, -1, 0, 0, 0)g_{-4}-\varepsilon_{2}+\varepsilon_{3}
Module 151(0, -1, 0, 0, 0, 0, 0)(0, -1, 0, 0, 0, 0, 0)g_{-2}\varepsilon_{1}+\varepsilon_{2}
Module 161(0, 1, 0, 0, 0, 0, 0)(0, 1, 0, 0, 0, 0, 0)g_{2}-\varepsilon_{1}-\varepsilon_{2}
Module 173(-1, -2, -2, -4, -3, -2, -1)(0, 0, 1, 0, 0, 0, 0)g_{3}
g_{8}
g_{-61}		\varepsilon_{1}-\varepsilon_{2}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 181(0, 0, 0, 1, 0, 0, 0)(0, 0, 0, 1, 0, 0, 0)g_{4}\varepsilon_{2}-\varepsilon_{3}
Module 191(0, 0, 0, 0, 1, 0, 0)(0, 0, 0, 0, 1, 0, 0)g_{5}\varepsilon_{3}-\varepsilon_{4}
Module 201(0, 0, 0, 0, 0, 1, 0)(0, 0, 0, 0, 0, 1, 0)g_{6}\varepsilon_{4}-\varepsilon_{5}
Module 211(0, 0, 0, 0, 0, 0, 1)(0, 0, 0, 0, 0, 0, 1)g_{7}\varepsilon_{5}-\varepsilon_{6}
Module 221(0, 1, 0, 1, 0, 0, 0)(0, 1, 0, 1, 0, 0, 0)g_{9}-\varepsilon_{1}-\varepsilon_{3}
Module 233(-1, -2, -2, -3, -3, -2, -1)(0, 0, 1, 1, 0, 0, 0)g_{10}
g_{14}
g_{-60}		\varepsilon_{1}-\varepsilon_{3}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 241(0, 0, 0, 1, 1, 0, 0)(0, 0, 0, 1, 1, 0, 0)g_{11}\varepsilon_{2}-\varepsilon_{4}
Module 251(0, 0, 0, 0, 1, 1, 0)(0, 0, 0, 0, 1, 1, 0)g_{12}\varepsilon_{3}-\varepsilon_{5}
Module 261(0, 0, 0, 0, 0, 1, 1)(0, 0, 0, 0, 0, 1, 1)g_{13}\varepsilon_{4}-\varepsilon_{6}
Module 273(-1, -1, -2, -3, -3, -2, -1)(0, 1, 1, 1, 0, 0, 0)g_{15}
g_{20}
g_{-59}		-\varepsilon_{2}-\varepsilon_{3}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 281(0, 1, 0, 1, 1, 0, 0)(0, 1, 0, 1, 1, 0, 0)g_{16}-\varepsilon_{1}-\varepsilon_{4}
Module 293(-1, -2, -2, -3, -2, -2, -1)(0, 0, 1, 1, 1, 0, 0)g_{17}
g_{21}
g_{-58}		\varepsilon_{1}-\varepsilon_{4}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 301(0, 0, 0, 1, 1, 1, 0)(0, 0, 0, 1, 1, 1, 0)g_{18}\varepsilon_{2}-\varepsilon_{5}
Module 311(0, 0, 0, 0, 1, 1, 1)(0, 0, 0, 0, 1, 1, 1)g_{19}\varepsilon_{3}-\varepsilon_{6}
Module 323(-1, -1, -2, -3, -2, -2, -1)(0, 1, 1, 1, 1, 0, 0)g_{22}
g_{26}
g_{-57}		-\varepsilon_{2}-\varepsilon_{4}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 331(0, 1, 0, 1, 1, 1, 0)(0, 1, 0, 1, 1, 1, 0)g_{23}-\varepsilon_{1}-\varepsilon_{5}
Module 343(-1, -2, -2, -3, -2, -1, -1)(0, 0, 1, 1, 1, 1, 0)g_{24}
g_{28}
g_{-56}		\varepsilon_{1}-\varepsilon_{5}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 351(0, 0, 0, 1, 1, 1, 1)(0, 0, 0, 1, 1, 1, 1)g_{25}\varepsilon_{2}-\varepsilon_{6}
Module 363(-1, -1, -2, -2, -2, -2, -1)(0, 1, 1, 2, 1, 0, 0)g_{27}
g_{32}
g_{-55}		-\varepsilon_{3}-\varepsilon_{4}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 373(-1, -1, -2, -3, -2, -1, -1)(0, 1, 1, 1, 1, 1, 0)g_{29}
g_{33}
g_{-54}		-\varepsilon_{2}-\varepsilon_{5}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 381(0, 1, 0, 1, 1, 1, 1)(0, 1, 0, 1, 1, 1, 1)g_{30}-\varepsilon_{1}-\varepsilon_{6}
Module 393(-1, -2, -2, -3, -2, -1, 0)(0, 0, 1, 1, 1, 1, 1)g_{31}
g_{35}
g_{-53}		\varepsilon_{1}-\varepsilon_{6}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 403(-1, -1, -2, -2, -2, -1, -1)(0, 1, 1, 2, 1, 1, 0)g_{34}
g_{38}
g_{-51}		-\varepsilon_{3}-\varepsilon_{5}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 413(-1, -1, -2, -3, -2, -1, 0)(0, 1, 1, 1, 1, 1, 1)g_{36}
g_{40}
g_{-50}		-\varepsilon_{2}-\varepsilon_{6}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 423(0, -1, -1, -2, -2, -2, -1)(1, 1, 2, 2, 1, 0, 0)g_{37}
g_{-52}
g_{-49}		1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{5}+\varepsilon_{6}
Module 433(-1, -1, -2, -2, -1, -1, -1)(0, 1, 1, 2, 2, 1, 0)g_{39}
g_{43}
g_{-47}		-\varepsilon_{4}-\varepsilon_{5}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 443(-1, -1, -2, -2, -2, -1, 0)(0, 1, 1, 2, 1, 1, 1)g_{41}
g_{44}
g_{-46}		-\varepsilon_{3}-\varepsilon_{6}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 453(0, -1, -1, -2, -2, -1, -1)(1, 1, 2, 2, 1, 1, 0)g_{42}
g_{-48}
g_{-45}		1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{4}+\varepsilon_{6}
Module 463(-1, -1, -2, -2, -1, -1, 0)(0, 1, 1, 2, 2, 1, 1)g_{45}
g_{48}
g_{-42}		-\varepsilon_{4}-\varepsilon_{6}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 473(0, -1, -1, -2, -1, -1, -1)(1, 1, 2, 2, 2, 1, 0)g_{46}
g_{-44}
g_{-41}		1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{3}+\varepsilon_{6}
Module 483(0, -1, -1, -2, -2, -1, 0)(1, 1, 2, 2, 1, 1, 1)g_{47}
g_{-43}
g_{-39}		1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{4}+\varepsilon_{5}
Module 493(-1, -1, -2, -2, -1, 0, 0)(0, 1, 1, 2, 2, 2, 1)g_{49}
g_{52}
g_{-37}		-\varepsilon_{5}-\varepsilon_{6}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 503(0, -1, -1, -1, -1, -1, -1)(1, 1, 2, 3, 2, 1, 0)g_{50}
g_{-40}
g_{-36}		1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{6}
Module 513(0, -1, -1, -2, -1, -1, 0)(1, 1, 2, 2, 2, 1, 1)g_{51}
g_{-38}
g_{-34}		1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{3}+\varepsilon_{5}
Module 523(0, 0, -1, -1, -1, -1, -1)(1, 2, 2, 3, 2, 1, 0)g_{53}
g_{-35}
g_{-31}		-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{1}+\varepsilon_{6}
Module 533(0, -1, -1, -1, -1, -1, 0)(1, 1, 2, 3, 2, 1, 1)g_{54}
g_{-33}
g_{-29}		1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{5}
Module 543(0, -1, -1, -2, -1, 0, 0)(1, 1, 2, 2, 2, 2, 1)g_{55}
g_{-32}
g_{-27}		1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{3}+\varepsilon_{4}
Module 553(0, 0, -1, -1, -1, -1, 0)(1, 2, 2, 3, 2, 1, 1)g_{56}
g_{-28}
g_{-24}		-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}+1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{1}+\varepsilon_{5}
Module 563(0, -1, -1, -1, -1, 0, 0)(1, 1, 2, 3, 2, 2, 1)g_{57}
g_{-26}
g_{-22}		1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{4}
Module 573(0, 0, -1, -1, -1, 0, 0)(1, 2, 2, 3, 2, 2, 1)g_{58}
g_{-21}
g_{-17}		-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}+1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{1}+\varepsilon_{4}
Module 583(0, -1, -1, -1, 0, 0, 0)(1, 1, 2, 3, 3, 2, 1)g_{59}
g_{-20}
g_{-15}		1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{2}+\varepsilon_{3}
Module 593(0, 0, -1, -1, 0, 0, 0)(1, 2, 2, 3, 3, 2, 1)g_{60}
g_{-14}
g_{-10}		-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}-1/2\varepsilon_{2}+1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{1}+\varepsilon_{3}
Module 603(0, 0, -1, 0, 0, 0, 0)(1, 2, 2, 4, 3, 2, 1)g_{61}
g_{-8}
g_{-3}		-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
-\varepsilon_{1}+\varepsilon_{2}
Module 618(-1, -2, -3, -4, -3, -2, -1)(1, 2, 3, 4, 3, 2, 1)g_{62}
g_{-1}
g_{63}
-h_{1}
h_{7}+2h_{6}+3h_{5}+4h_{4}+3h_{3}+2h_{2}+2h_{1}
g_{-63}
g_{1}
g_{-62}		1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
1/2\varepsilon_{1}-1/2\varepsilon_{2}-1/2\varepsilon_{3}-1/2\varepsilon_{4}-1/2\varepsilon_{5}-1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
\varepsilon_{7}-\varepsilon_{8}
0
0
-\varepsilon_{7}+\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}+1/2\varepsilon_{7}-1/2\varepsilon_{8}
-1/2\varepsilon_{1}+1/2\varepsilon_{2}+1/2\varepsilon_{3}+1/2\varepsilon_{4}+1/2\varepsilon_{5}+1/2\varepsilon_{6}-1/2\varepsilon_{7}+1/2\varepsilon_{8}
Module 621(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{2}0
Module 631(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{4}0
Module 641(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{5}0
Module 651(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{6}0
Module 661(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{7}0
Information about the subalgebra generation algorithm.
Heirs rejected due to having symmetric Cartan type outside of list dictated by parabolic heirs: 16
Heirs rejected due to not being maximally dominant: 43
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 43
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
Parabolically induced by A^{1}_1
Potential Dynkin type extensions: A^{1}_3, A^{1}_2+A^{1}_1,