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Representations of reductive groups over finite local rings of length two.

Stasinski, Alexander and Vera-Gajardo, Andrea (2019) 'Representations of reductive groups over finite local rings of length two.', Journal of algebra., 525 . pp. 171-190.


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))].

Item Type:Article
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Publisher statement:© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:14 December 2018
Date deposited:06 February 2019
Date of first online publication:14 December 2018
Date first made open access:14 December 2019

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