Representations of Finite Chevalley Groups: A Survey |
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A-modules abelian groups action affine variety bijection Borel subgroup category of sheaves centralizer algebra Chapter character of GF class functions classical groups cohomology groups conjugacy classes constant sheaf corresponds cuspidal representation defined Definition denote dimension elements of G étale exact sequence example F-stable maximal torus F-stable parabolic subgroup fibre finite group follows formula Frobenius morphism functor geometric point hence homomorphism IndGF induced integer irreducible representation isomorphic l-adic cohomology Lemma Let G Lie algebra Lusztig maximal torus morphism f nilpotent open set orthogonality parabolic subgroup Proof Proposition quotient regular subgroup Remark representations of GF semisimple semisimple element sheaves of abelian Spec stalk standard Frobenius subgroup of G subset Suppose Theorem topology tori unipotent cuspidal representation unipotent elements unipotent representations virtual representations Weyl group θε χε