Bounds on multiplicities of spherical spaces over finite fields

Avraham Aizenbud; Nir Avni

doi:10.1016/j.jpaa.2018.12.008

Bounds on multiplicities of spherical spaces over finite fields

Avraham Aizenbud, Nir Avni^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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].

Original language	English (US)
Pages (from-to)	3859-3868
Number of pages	10
Journal	Journal of Pure and Applied Algebra
Volume	223
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2018.12.008
State	Published - Sep 2019

Funding

A.A. was partially supported by ISF grant 687/13 and a Minerva Foundation grant. N.A. was partially supported by NSF grant DMS-1303205. Both of us were partially supported by BSF grant 2012247.

Keywords

Representations of groups of Lie type

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2018.12.008

Cite this

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AU - Avni, Nir

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N2 - 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].

AB - 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].

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Bounds on multiplicities of spherical spaces over finite fields

Abstract

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