## Representations of Finite Chevalley Groups: A Survey |

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### Contents

INTRODUCTION | 1 |

CLASSIFICATION OF TORI | 8 |

PRINCIPAL SERIES REPRESENTATIONS | 21 |

Copyright | |

6 other sections not shown

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### Common terms and phrases

A-modules abelian groups action of H affine variety bijection Borel subgroup Bruhat decomposition category of sheaves centralizer algebra Chapter class functions classical groups cohomology groups commutative diagram conjugacy classes constant sheaf corresponds cuspidal representation defined Definition denote dimension elements of G exact sequence example F acts F-stable maximal torus F-stable parabolic subgroup finite group follows formula Frobenius morphism functor geometric point given group G H X,Q hence homomorphism induced integer irreducible representations isomorphic Lemma Let G Lie algebra Lusztig maximal torus morphism f nilpotent open set orthogonality parabolic subgroup presheaf Proof Proposition quotient regular subgroup Remark representations of G semisimple semisimple elements sheaves of abelian Spec stalk standard Frobenius subgroup of G subset subspace Suppose Theorem topology tori torus of G unipotent cuspidal representation unipotent elements unipotent representations virtual representations Weyl group