Simple Weight Modules of Complex Reductive Lie Algebras |
Contents
CONVEX SUBSETS OF ROOT SYSTEMS | 5 |
CONSTRUCTION OF ARBITRARY SIMPLE WEIGHT | 18 |
HEISENBERG LIE ALGEBRAS FROM SIMPLE | 51 |
3 other sections not shown
Common terms and phrases
_-module acts assertion associated assume B₁ base basis called Cartan subalgebra chapter closed commutation Consequently construct containing convex Corollary corresponding decomposition define denote determined dimension direct sum elements exists fact filtration Finally finite dimensional complex finite length finite type follows h₁ hand Heisenberg Lie algebra implies induction integers isomorphism Lemma linear M₁ M₂ modules with property nilpotent nonzero Note observe pair parabolic subalgebra parabolic subset positive Proof property TF Proposition Proposition 4.3 prove Q-closed Recall reductive Lie algebra relations representation respect result root system semisimple simple Lie algebra simple weight module space structure subalgebra of g submodule subspace subsystem Suppose symmetric symplectic basis t₁ T₂ Table Theorem translate weight space weight vectors Weyl α α