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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Alexander Stasinski

Stasinski, Alexander & Vera-Gajardo, Andrea (2019). Representations of reductive groups over finite local rings of length two. Journal of Algebra 525: 171-190.

Author(s) from Durham

Abstract

LetFqbe a finite field of characteristicp, and letW2(Fq)be thering of Witt vectors of length two overFq. We prove that for any reduc-tive group schemeGoverZsuch thatpis very good forG×Fq, the groupsG(Fq[t]/t2)andG(W2(Fq))have the same number of irreducible representa-tions of dimensiond, for eachd. Equivalently, there exists an isomorphism ofgroup algebrasC[G(Fq[t]/t2)]∼=C[G(W2(Fq))].