Irreducibility of Infinite Dimensional Steinberg Modules of Reductive Groups with Frobenius Maps

2015/07/14 by Ruotao Yang, Yang, Ruotao · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #math.RT

paper · pdf · doi:10.48550/arxiv.1507.03795

9 pages

arxiv created 2015/07/16 · arxiv updated 2015/07/17

Abstract

Let G be a connected reductive group over an algebraic closure of a finite field Fq. In this paper it is proved that the infinite dimensional Steinberg module of kG defined by N. Xi in 2014 is irreducible when k is a field of positive characteristic and char k is not char Fq. For certain special linear groups, we show that the Steinberg modules of the groups are not quasi-finite with respect to some natural quasi-finite sequences of the groups.

Cited by

• Irreducibility of Certain Subquotients of Spherical Principal Series Representations of Reductive Groups with Frobenius Maps

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