Bounds on multiplicities of spherical spaces over finite fields -- the general case

2019/12/08 by Shai Shechter, Shechter, Shai
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1912.03694

openalex publication_date 2019/12/08 · openalex created_date 2019/12/13 · openalex updated_date 2026/07/28

Abstract

Let G be a connected reductive group scheme acting on a spherical scheme X. In the case where G is of type A_n, Aizenbud and Avni proved the existence of a number C such that the multiplicity dim\hom(ρ,ℂ[X(F)]) is bounded by C, for any finite field F and any irreducible representation ρ of G(F). In this paper, we generalize this result to the case where G is a connected reductive group scheme over ℤ, and prove Conjecture A of [1].

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