Bounds on multiplicities of symmetric pairs of finite groups

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Abstract

Let Γ be a finite group, let θ be an involution of Γ and let p be an irreducible complex representation of Γ. We bound dimpΓθ in terms of the smallest dimension of a faithful Fp-representation of Γ/Radp(Γ), where p is any odd prime and Radp(Γ) is the maximal normal p-subgroup of Γ. This implies, in particular, that if G is a group scheme over Z and θ is an involution of G, then the multiplicity of any irreducible representation in C∞(G(Zp)/Gθ(Zp)) is bounded, uniformly in p.

Original languageEnglish
Article numbere73
JournalForum of Mathematics, Sigma
Volume12
DOIs
StatePublished - 9 Sep 2024

All Science Journal Classification (ASJC) codes

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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