LECTURE 8: REPRESENTATIONS OF gF AND OF GLn(Fq)
نویسنده
چکیده
We start by briefly explaining key results on the representation theory of semisimple Lie algebras in large enough positive characteristic. After that, we start a new topic: the complex representation theory of finite groups of Lie type and Hecke algebras. Today we consider the most basic group: G := GLn(Fq). We introduce the Hecke algebra as the endomorphism algebra of the G-module C[B \ G]. We describe the basis in this algebra and some of the multiplication rules that allow to present the Hecke algebra by generators and relations. Then we use the Tits deformation principle to show that the Hecke algebra is isomorphic to CSn.
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