Character Theory for Semilinear Representations

2025/11/06 by James A. Taylor, Taylor, James
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2511.04296

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

Let G be a group acting on a field L, and suppose that L /L^G is a finite extension. We show that the category of semilinear representations of G over L can be described in terms of the category of linear representations of H, the kernel of the map G → Aut(L). When G is finite and L has characteristic 0 this provides a character theory for semilinear representations of G over L, which recovers ordinary character theory when the action of G on L is trivial.

Citations

• The Categories of Lubin-Tate and Drinfeld Bundles
• Brauer's 14th Problem and Dyson's Tenfold Way
• Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces
• On representations of twisted group rings

Related

• Regular characters of GL_n(O) and Weil representations over finite fields
• Representation Theory of Finite Groups
• Determining Aschbacher classes using characters
• Harmonic Analysis on GL(n) over Finite Fields
• Four Drafts of The Representation Theory of the Group of Infinite Matrices over Finite Fields