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arXiv · 1507.03795

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

Ruotao Yang
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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.

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BibTeXRIS

Ruotao Yang. 2015-07-14. Irreducibility of Infinite Dimensional Steinberg Modules of Reductive Groups with Frobenius Maps. https://arxiv.org/abs/1507.03795

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