Representations of reductive groups over finite rings and extended Deligne-Lusztig varieties

2004/03/28 by Alexander Stasinski, Stasinski, Alexander
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.math/0403487

10 pages

arxiv created 2004/03/28 · arxiv updated 2009/12/01

Abstract

In a previous paper it was shown that a certain family of varieties suggested by Lusztig, is not enough to construct all irreducible complex representations of reductive groups over finite rings coming from the ring of integers in a local field, modulo a power of the maximal ideal. In this paper we define a generalisation of Lusztig's varieties, corresponding to an extension of the maximal unramified extension of the local field. We show in a particular case that all irreducible representations appear in the cohomology of some extended variety. We conclude with a discussion about reformulation of Lusztig's conjecture.

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