Let G be a reductive group scheme of type A acting on a spherical scheme X. We prove that there exists a number C such that the multiplicity dimHom(ρ,C[X(F)]) is bounded by C, for any finite field F and any irreducible representation ρ of G(F). We give an explicit bound for C. We conjecture that this result is true for any reductive group scheme and when F ranges (in addition) over all local fields of characteristic 0. Different aspects of this conjecture were studied in [3,11,6,7].
- Representations of groups of Lie type
ASJC Scopus subject areas
- Algebra and Number Theory