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 language | English |
---|---|
Article number | e73 |
Journal | Forum of Mathematics, Sigma |
Volume | 12 |
DOIs | |
State | Published - 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