Type: \(\displaystyle 0\) (Dynkin type computed to be: \(\displaystyle 0\))
Simple basis: 0 vectors:
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}: E^{1}_7
simple basis centralizer: 7 vectors: (1, 0, 0, 0, 0, 0, 0), (0, 0, 1, 0, 0, 0, 0), (0, 0, 0, 1, 0, 0, 0), (0, 1, 0, 0, 0, 0, 0), (0, 0, 0, 0, 1, 0, 0), (0, 0, 0, 0, 0, 0, 1), (0, 0, 0, 0, 0, 1, 0)
Number of k-submodules of g: 133
Module decomposition, fundamental coords over k: \(\displaystyle 133V_{0}\)
g/k k-submodules
idsizeb\cap k-lowest weightb\cap k-highest weightModule basisWeights epsilon coords
Module 11(-2, -2, -3, -4, -3, -2, -1)(-2, -2, -3, -4, -3, -2, -1)g_{-63}-\varepsilon_{7}+\varepsilon_{8}
Module 21(-1, -2, -3, -4, -3, -2, -1)(-1, -2, -3, -4, -3, -2, -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}
Module 31(-1, -2, -2, -4, -3, -2, -1)(-1, -2, -2, -4, -3, -2, -1)g_{-61}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 41(-1, -2, -2, -3, -3, -2, -1)(-1, -2, -2, -3, -3, -2, -1)g_{-60}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 51(-1, -1, -2, -3, -3, -2, -1)(-1, -1, -2, -3, -3, -2, -1)g_{-59}-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 61(-1, -2, -2, -3, -2, -2, -1)(-1, -2, -2, -3, -2, -2, -1)g_{-58}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 71(-1, -1, -2, -3, -2, -2, -1)(-1, -1, -2, -3, -2, -2, -1)g_{-57}-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 81(-1, -2, -2, -3, -2, -1, -1)(-1, -2, -2, -3, -2, -1, -1)g_{-56}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 91(-1, -1, -2, -2, -2, -2, -1)(-1, -1, -2, -2, -2, -2, -1)g_{-55}-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 101(-1, -1, -2, -3, -2, -1, -1)(-1, -1, -2, -3, -2, -1, -1)g_{-54}-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 111(-1, -2, -2, -3, -2, -1, 0)(-1, -2, -2, -3, -2, -1, 0)g_{-53}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 121(-1, -1, -1, -2, -2, -2, -1)(-1, -1, -1, -2, -2, -2, -1)g_{-52}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 131(-1, -1, -2, -2, -2, -1, -1)(-1, -1, -2, -2, -2, -1, -1)g_{-51}-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 141(-1, -1, -2, -3, -2, -1, 0)(-1, -1, -2, -3, -2, -1, 0)g_{-50}-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 151(0, -1, -1, -2, -2, -2, -1)(0, -1, -1, -2, -2, -2, -1)g_{-49}\varepsilon_{5}+\varepsilon_{6}
Module 161(-1, -1, -1, -2, -2, -1, -1)(-1, -1, -1, -2, -2, -1, -1)g_{-48}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 171(-1, -1, -2, -2, -1, -1, -1)(-1, -1, -2, -2, -1, -1, -1)g_{-47}-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(-1, -1, -2, -2, -2, -1, 0)(-1, -1, -2, -2, -2, -1, 0)g_{-46}-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 191(0, -1, -1, -2, -2, -1, -1)(0, -1, -1, -2, -2, -1, -1)g_{-45}\varepsilon_{4}+\varepsilon_{6}
Module 201(-1, -1, -1, -2, -1, -1, -1)(-1, -1, -1, -2, -1, -1, -1)g_{-44}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 211(-1, -1, -1, -2, -2, -1, 0)(-1, -1, -1, -2, -2, -1, 0)g_{-43}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 221(-1, -1, -2, -2, -1, -1, 0)(-1, -1, -2, -2, -1, -1, 0)g_{-42}-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 231(0, -1, -1, -2, -1, -1, -1)(0, -1, -1, -2, -1, -1, -1)g_{-41}\varepsilon_{3}+\varepsilon_{6}
Module 241(-1, -1, -1, -1, -1, -1, -1)(-1, -1, -1, -1, -1, -1, -1)g_{-40}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 251(0, -1, -1, -2, -2, -1, 0)(0, -1, -1, -2, -2, -1, 0)g_{-39}\varepsilon_{4}+\varepsilon_{5}
Module 261(-1, -1, -1, -2, -1, -1, 0)(-1, -1, -1, -2, -1, -1, 0)g_{-38}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 271(-1, -1, -2, -2, -1, 0, 0)(-1, -1, -2, -2, -1, 0, 0)g_{-37}-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, -1, -1, -1, -1, -1)(0, -1, -1, -1, -1, -1, -1)g_{-36}\varepsilon_{2}+\varepsilon_{6}
Module 291(-1, 0, -1, -1, -1, -1, -1)(-1, 0, -1, -1, -1, -1, -1)g_{-35}-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, -1, -1, -2, -1, -1, 0)(0, -1, -1, -2, -1, -1, 0)g_{-34}\varepsilon_{3}+\varepsilon_{5}
Module 311(-1, -1, -1, -1, -1, -1, 0)(-1, -1, -1, -1, -1, -1, 0)g_{-33}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 321(-1, -1, -1, -2, -1, 0, 0)(-1, -1, -1, -2, -1, 0, 0)g_{-32}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, 0, -1, -1, -1, -1, -1)(0, 0, -1, -1, -1, -1, -1)g_{-31}-\varepsilon_{1}+\varepsilon_{6}
Module 341(0, -1, 0, -1, -1, -1, -1)(0, -1, 0, -1, -1, -1, -1)g_{-30}\varepsilon_{1}+\varepsilon_{6}
Module 351(0, -1, -1, -1, -1, -1, 0)(0, -1, -1, -1, -1, -1, 0)g_{-29}\varepsilon_{2}+\varepsilon_{5}
Module 361(-1, 0, -1, -1, -1, -1, 0)(-1, 0, -1, -1, -1, -1, 0)g_{-28}-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 371(0, -1, -1, -2, -1, 0, 0)(0, -1, -1, -2, -1, 0, 0)g_{-27}\varepsilon_{3}+\varepsilon_{4}
Module 381(-1, -1, -1, -1, -1, 0, 0)(-1, -1, -1, -1, -1, 0, 0)g_{-26}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 391(0, 0, 0, -1, -1, -1, -1)(0, 0, 0, -1, -1, -1, -1)g_{-25}-\varepsilon_{2}+\varepsilon_{6}
Module 401(0, 0, -1, -1, -1, -1, 0)(0, 0, -1, -1, -1, -1, 0)g_{-24}-\varepsilon_{1}+\varepsilon_{5}
Module 411(0, -1, 0, -1, -1, -1, 0)(0, -1, 0, -1, -1, -1, 0)g_{-23}\varepsilon_{1}+\varepsilon_{5}
Module 421(0, -1, -1, -1, -1, 0, 0)(0, -1, -1, -1, -1, 0, 0)g_{-22}\varepsilon_{2}+\varepsilon_{4}
Module 431(-1, 0, -1, -1, -1, 0, 0)(-1, 0, -1, -1, -1, 0, 0)g_{-21}-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 441(-1, -1, -1, -1, 0, 0, 0)(-1, -1, -1, -1, 0, 0, 0)g_{-20}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 451(0, 0, 0, 0, -1, -1, -1)(0, 0, 0, 0, -1, -1, -1)g_{-19}-\varepsilon_{3}+\varepsilon_{6}
Module 461(0, 0, 0, -1, -1, -1, 0)(0, 0, 0, -1, -1, -1, 0)g_{-18}-\varepsilon_{2}+\varepsilon_{5}
Module 471(0, 0, -1, -1, -1, 0, 0)(0, 0, -1, -1, -1, 0, 0)g_{-17}-\varepsilon_{1}+\varepsilon_{4}
Module 481(0, -1, 0, -1, -1, 0, 0)(0, -1, 0, -1, -1, 0, 0)g_{-16}\varepsilon_{1}+\varepsilon_{4}
Module 491(0, -1, -1, -1, 0, 0, 0)(0, -1, -1, -1, 0, 0, 0)g_{-15}\varepsilon_{2}+\varepsilon_{3}
Module 501(-1, 0, -1, -1, 0, 0, 0)(-1, 0, -1, -1, 0, 0, 0)g_{-14}-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 511(0, 0, 0, 0, 0, -1, -1)(0, 0, 0, 0, 0, -1, -1)g_{-13}-\varepsilon_{4}+\varepsilon_{6}
Module 521(0, 0, 0, 0, -1, -1, 0)(0, 0, 0, 0, -1, -1, 0)g_{-12}-\varepsilon_{3}+\varepsilon_{5}
Module 531(0, 0, 0, -1, -1, 0, 0)(0, 0, 0, -1, -1, 0, 0)g_{-11}-\varepsilon_{2}+\varepsilon_{4}
Module 541(0, 0, -1, -1, 0, 0, 0)(0, 0, -1, -1, 0, 0, 0)g_{-10}-\varepsilon_{1}+\varepsilon_{3}
Module 551(0, -1, 0, -1, 0, 0, 0)(0, -1, 0, -1, 0, 0, 0)g_{-9}\varepsilon_{1}+\varepsilon_{3}
Module 561(-1, 0, -1, 0, 0, 0, 0)(-1, 0, -1, 0, 0, 0, 0)g_{-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 571(0, 0, 0, 0, 0, 0, -1)(0, 0, 0, 0, 0, 0, -1)g_{-7}-\varepsilon_{5}+\varepsilon_{6}
Module 581(0, 0, 0, 0, 0, -1, 0)(0, 0, 0, 0, 0, -1, 0)g_{-6}-\varepsilon_{4}+\varepsilon_{5}
Module 591(0, 0, 0, 0, -1, 0, 0)(0, 0, 0, 0, -1, 0, 0)g_{-5}-\varepsilon_{3}+\varepsilon_{4}
Module 601(0, 0, 0, -1, 0, 0, 0)(0, 0, 0, -1, 0, 0, 0)g_{-4}-\varepsilon_{2}+\varepsilon_{3}
Module 611(0, 0, -1, 0, 0, 0, 0)(0, 0, -1, 0, 0, 0, 0)g_{-3}-\varepsilon_{1}+\varepsilon_{2}
Module 621(0, -1, 0, 0, 0, 0, 0)(0, -1, 0, 0, 0, 0, 0)g_{-2}\varepsilon_{1}+\varepsilon_{2}
Module 631(-1, 0, 0, 0, 0, 0, 0)(-1, 0, 0, 0, 0, 0, 0)g_{-1}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 641(1, 0, 0, 0, 0, 0, 0)(1, 0, 0, 0, 0, 0, 0)g_{1}-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 651(0, 1, 0, 0, 0, 0, 0)(0, 1, 0, 0, 0, 0, 0)g_{2}-\varepsilon_{1}-\varepsilon_{2}
Module 661(0, 0, 1, 0, 0, 0, 0)(0, 0, 1, 0, 0, 0, 0)g_{3}\varepsilon_{1}-\varepsilon_{2}
Module 671(0, 0, 0, 1, 0, 0, 0)(0, 0, 0, 1, 0, 0, 0)g_{4}\varepsilon_{2}-\varepsilon_{3}
Module 681(0, 0, 0, 0, 1, 0, 0)(0, 0, 0, 0, 1, 0, 0)g_{5}\varepsilon_{3}-\varepsilon_{4}
Module 691(0, 0, 0, 0, 0, 1, 0)(0, 0, 0, 0, 0, 1, 0)g_{6}\varepsilon_{4}-\varepsilon_{5}
Module 701(0, 0, 0, 0, 0, 0, 1)(0, 0, 0, 0, 0, 0, 1)g_{7}\varepsilon_{5}-\varepsilon_{6}
Module 711(1, 0, 1, 0, 0, 0, 0)(1, 0, 1, 0, 0, 0, 0)g_{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 721(0, 1, 0, 1, 0, 0, 0)(0, 1, 0, 1, 0, 0, 0)g_{9}-\varepsilon_{1}-\varepsilon_{3}
Module 731(0, 0, 1, 1, 0, 0, 0)(0, 0, 1, 1, 0, 0, 0)g_{10}\varepsilon_{1}-\varepsilon_{3}
Module 741(0, 0, 0, 1, 1, 0, 0)(0, 0, 0, 1, 1, 0, 0)g_{11}\varepsilon_{2}-\varepsilon_{4}
Module 751(0, 0, 0, 0, 1, 1, 0)(0, 0, 0, 0, 1, 1, 0)g_{12}\varepsilon_{3}-\varepsilon_{5}
Module 761(0, 0, 0, 0, 0, 1, 1)(0, 0, 0, 0, 0, 1, 1)g_{13}\varepsilon_{4}-\varepsilon_{6}
Module 771(1, 0, 1, 1, 0, 0, 0)(1, 0, 1, 1, 0, 0, 0)g_{14}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 781(0, 1, 1, 1, 0, 0, 0)(0, 1, 1, 1, 0, 0, 0)g_{15}-\varepsilon_{2}-\varepsilon_{3}
Module 791(0, 1, 0, 1, 1, 0, 0)(0, 1, 0, 1, 1, 0, 0)g_{16}-\varepsilon_{1}-\varepsilon_{4}
Module 801(0, 0, 1, 1, 1, 0, 0)(0, 0, 1, 1, 1, 0, 0)g_{17}\varepsilon_{1}-\varepsilon_{4}
Module 811(0, 0, 0, 1, 1, 1, 0)(0, 0, 0, 1, 1, 1, 0)g_{18}\varepsilon_{2}-\varepsilon_{5}
Module 821(0, 0, 0, 0, 1, 1, 1)(0, 0, 0, 0, 1, 1, 1)g_{19}\varepsilon_{3}-\varepsilon_{6}
Module 831(1, 1, 1, 1, 0, 0, 0)(1, 1, 1, 1, 0, 0, 0)g_{20}-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 841(1, 0, 1, 1, 1, 0, 0)(1, 0, 1, 1, 1, 0, 0)g_{21}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 851(0, 1, 1, 1, 1, 0, 0)(0, 1, 1, 1, 1, 0, 0)g_{22}-\varepsilon_{2}-\varepsilon_{4}
Module 861(0, 1, 0, 1, 1, 1, 0)(0, 1, 0, 1, 1, 1, 0)g_{23}-\varepsilon_{1}-\varepsilon_{5}
Module 871(0, 0, 1, 1, 1, 1, 0)(0, 0, 1, 1, 1, 1, 0)g_{24}\varepsilon_{1}-\varepsilon_{5}
Module 881(0, 0, 0, 1, 1, 1, 1)(0, 0, 0, 1, 1, 1, 1)g_{25}\varepsilon_{2}-\varepsilon_{6}
Module 891(1, 1, 1, 1, 1, 0, 0)(1, 1, 1, 1, 1, 0, 0)g_{26}-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 901(0, 1, 1, 2, 1, 0, 0)(0, 1, 1, 2, 1, 0, 0)g_{27}-\varepsilon_{3}-\varepsilon_{4}
Module 911(1, 0, 1, 1, 1, 1, 0)(1, 0, 1, 1, 1, 1, 0)g_{28}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 921(0, 1, 1, 1, 1, 1, 0)(0, 1, 1, 1, 1, 1, 0)g_{29}-\varepsilon_{2}-\varepsilon_{5}
Module 931(0, 1, 0, 1, 1, 1, 1)(0, 1, 0, 1, 1, 1, 1)g_{30}-\varepsilon_{1}-\varepsilon_{6}
Module 941(0, 0, 1, 1, 1, 1, 1)(0, 0, 1, 1, 1, 1, 1)g_{31}\varepsilon_{1}-\varepsilon_{6}
Module 951(1, 1, 1, 2, 1, 0, 0)(1, 1, 1, 2, 1, 0, 0)g_{32}-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 961(1, 1, 1, 1, 1, 1, 0)(1, 1, 1, 1, 1, 1, 0)g_{33}-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 971(0, 1, 1, 2, 1, 1, 0)(0, 1, 1, 2, 1, 1, 0)g_{34}-\varepsilon_{3}-\varepsilon_{5}
Module 981(1, 0, 1, 1, 1, 1, 1)(1, 0, 1, 1, 1, 1, 1)g_{35}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 991(0, 1, 1, 1, 1, 1, 1)(0, 1, 1, 1, 1, 1, 1)g_{36}-\varepsilon_{2}-\varepsilon_{6}
Module 1001(1, 1, 2, 2, 1, 0, 0)(1, 1, 2, 2, 1, 0, 0)g_{37}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 1011(1, 1, 1, 2, 1, 1, 0)(1, 1, 1, 2, 1, 1, 0)g_{38}-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 1021(0, 1, 1, 2, 2, 1, 0)(0, 1, 1, 2, 2, 1, 0)g_{39}-\varepsilon_{4}-\varepsilon_{5}
Module 1031(1, 1, 1, 1, 1, 1, 1)(1, 1, 1, 1, 1, 1, 1)g_{40}-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 1041(0, 1, 1, 2, 1, 1, 1)(0, 1, 1, 2, 1, 1, 1)g_{41}-\varepsilon_{3}-\varepsilon_{6}
Module 1051(1, 1, 2, 2, 1, 1, 0)(1, 1, 2, 2, 1, 1, 0)g_{42}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 1061(1, 1, 1, 2, 2, 1, 0)(1, 1, 1, 2, 2, 1, 0)g_{43}-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 1071(1, 1, 1, 2, 1, 1, 1)(1, 1, 1, 2, 1, 1, 1)g_{44}-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 1081(0, 1, 1, 2, 2, 1, 1)(0, 1, 1, 2, 2, 1, 1)g_{45}-\varepsilon_{4}-\varepsilon_{6}
Module 1091(1, 1, 2, 2, 2, 1, 0)(1, 1, 2, 2, 2, 1, 0)g_{46}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 1101(1, 1, 2, 2, 1, 1, 1)(1, 1, 2, 2, 1, 1, 1)g_{47}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 1111(1, 1, 1, 2, 2, 1, 1)(1, 1, 1, 2, 2, 1, 1)g_{48}-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 1121(0, 1, 1, 2, 2, 2, 1)(0, 1, 1, 2, 2, 2, 1)g_{49}-\varepsilon_{5}-\varepsilon_{6}
Module 1131(1, 1, 2, 3, 2, 1, 0)(1, 1, 2, 3, 2, 1, 0)g_{50}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 1141(1, 1, 2, 2, 2, 1, 1)(1, 1, 2, 2, 2, 1, 1)g_{51}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 1151(1, 1, 1, 2, 2, 2, 1)(1, 1, 1, 2, 2, 2, 1)g_{52}-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 1161(1, 2, 2, 3, 2, 1, 0)(1, 2, 2, 3, 2, 1, 0)g_{53}-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 1171(1, 1, 2, 3, 2, 1, 1)(1, 1, 2, 3, 2, 1, 1)g_{54}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 1181(1, 1, 2, 2, 2, 2, 1)(1, 1, 2, 2, 2, 2, 1)g_{55}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 1191(1, 2, 2, 3, 2, 1, 1)(1, 2, 2, 3, 2, 1, 1)g_{56}-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 1201(1, 1, 2, 3, 2, 2, 1)(1, 1, 2, 3, 2, 2, 1)g_{57}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 1211(1, 2, 2, 3, 2, 2, 1)(1, 2, 2, 3, 2, 2, 1)g_{58}-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 1221(1, 1, 2, 3, 3, 2, 1)(1, 1, 2, 3, 3, 2, 1)g_{59}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 1231(1, 2, 2, 3, 3, 2, 1)(1, 2, 2, 3, 3, 2, 1)g_{60}-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 1241(1, 2, 2, 4, 3, 2, 1)(1, 2, 2, 4, 3, 2, 1)g_{61}-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 1251(1, 2, 3, 4, 3, 2, 1)(1, 2, 3, 4, 3, 2, 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}
Module 1261(2, 2, 3, 4, 3, 2, 1)(2, 2, 3, 4, 3, 2, 1)g_{63}\varepsilon_{7}-\varepsilon_{8}
Module 1271(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{1}0
Module 1281(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{2}0
Module 1291(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{3}0
Module 1301(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{4}0
Module 1311(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{5}0
Module 1321(0, 0, 0, 0, 0, 0, 0)(0, 0, 0, 0, 0, 0, 0)h_{6}0
Module 1331(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: 0
Heirs rejected due to not being maximally dominant: 125
Heirs rejected due to not being maximal with respect to small Dynkin diagram automorphism that extends to ambient automorphism: 125
Heirs rejected due to having ambient Lie algebra decomposition iso to an already found subalgebra: 0
This subalgebra is not parabolically induced by anyone
Potential Dynkin type extensions: A^{1}_1,