Bounds on multiplicities of spherical spaces over finite fields

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 thi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of pure and applied algebra 2019-09, Vol.223 (9), p.3859-3868
Main Authors: Aizenbud, Avraham, Avni, Nir
Format: Article
Language:English
Subjects:
Representations of groups of Lie type
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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].
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2018.12.008