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Representations of reductive groups over finite local rings of length two

Stasinski, Alexander; Vera-Gajardo, Andrea

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Authors

Andrea Vera-Gajardo



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))].

Citation

Stasinski, A., & Vera-Gajardo, A. (2019). Representations of reductive groups over finite local rings of length two. Journal of Algebra, 525, 171-190. https://doi.org/10.1016/j.jalgebra.2018.11.039

Journal Article Type Article
Acceptance Date Dec 14, 2018
Online Publication Date Dec 14, 2018
Publication Date May 1, 2019
Deposit Date Dec 27, 2018
Publicly Available Date Mar 28, 2024
Journal Journal of Algebra
Print ISSN 0021-8693
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 525
Pages 171-190
DOI https://doi.org/10.1016/j.jalgebra.2018.11.039

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