A parametrization of unipotent representations

IF 0.2 Q4 MATHEMATICS Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2021-11-16 DOI:10.21915/bimas.2022301

G. Lusztig

引用次数: 2

Abstract

0.1. Let G be a simple algebraic group defined and split over a finite field Fq. Let U be the set of isomorphism classes of irreducible unipotent representations (over C) of the finite group G(Fq). Let W be the Weyl group of G and let Irr(W ) be the set of isomorphism classes of irreducible representations (over C) of W . In [L79] a partition of Irr(W ) into families is described and in [L84] a partition U = ⊔cUc of U (with c running over the families of Irr(W )) is introduced. Moreover, in [L84, §4] to any family c we have associated a finite group Gc and a bijection

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幂函数表示的参数化

0.1. 设G是在有限域Fq上定义并分裂的一个简单代数群。设U是有限群G(Fq)在C上的不可约单幂表示的同构类的集合。设W是G的Weyl群，设Irr(W)是W的不可约表示的同构类的集合。在[L79]中描述了Irr(W)的族划分，并在[L84]中引入了U的U = * * cUc划分(其中c在Irr(W)的族上运行)。此外，在[L84，§4]中，我们把有限群Gc和双射联系在一起

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Bulletin of the Institute of Mathematics Academia Sinica New Series MATHEMATICS-

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