On Speh representations for level zero supercuspidal representations and Ginzburg-Kaplan gamma factors

2024/08/03 by Elad Zelingher, Zelingher, Elad
Mathematics · #11F66 #11F70 #20C33 #22E50 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2408.01856

openalex publication_date 2024/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a relation between Speh representations of GL_n(\mathbbF_q) and Speh representations of GL_n(F), where F is a non-archimedean local field. We use irreducible level zero supercuspidal representations to show that these two notions of Speh representations associated to cuspidal representations are related via a commutative diagram, and that their corresponding (k,c) ψ-Whittaker models are also related. We use these results to relate the local Ginzburg-Kaplan integrals for level zero supercuspidal representations to their finite field counterparts.

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