Representations of reductive groups over finite local rings of length two

Stasinski, Alexander; Vera-Gajardo, Andrea

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: Dec 14, 2019
• Journal: Journal of Algebra
• Print ISSN: 0021-8693
• Electronic ISSN: 1090-266X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 525
• Pages: 171-190
• DOI: https://doi.org/10.1016/j.jalgebra.2018.11.039
• Public URL: https://durham-repository.worktribe.com/output/1311145