Unipotent representations: changing q to -q

2025/08/19 by Pierre Deligne, Deligne, P., G. Lusztig +1
Computer Science · Mathematics · #FOS: Mathematics #Mathematics and Applications #Matrix Theory and Algorithms #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2508.13951

openalex publication_date 2025/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a Chevalley group over a finite field F_q such that the longest element of the Weyl group is central. We construct an involution ξ↦ξ^! of the set of unipotent representations of this group such that the degree polynomial of a unipotent representation ξ is obtained up to sign from the degree polynomial of ξ^! by changing q to -q.

Related

• Unipotent representations: changing q to -q, II
• Parametrizing unipotent representations
• A parametrization of unipotent representations
• Springer's work on unipotent classes and Weyl group representations
• Descents of unipotent representations of finite unitary groups