Bounds on multiplicities of spherical spaces over finite fields

Avraham Aizenbud, Nir Avni*

*Corresponding author for this work

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)3859-3868
Number of pages10
JournalJournal of Pure and Applied Algebra
Volume223
Issue number9
DOIs
StatePublished - Sep 1 2019

Fingerprint

Group Scheme
Reductive Group
Galois field
Multiplicity
Explicit Bounds
Local Field
Irreducible Representation
Range of data

Keywords

  • Representations of groups of Lie type

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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Bounds on multiplicities of spherical spaces over finite fields. / Aizenbud, Avraham; Avni, Nir.

In: Journal of Pure and Applied Algebra, Vol. 223, No. 9, 01.09.2019, p. 3859-3868.

Research output: Contribution to journalArticle

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AU - Avni, Nir

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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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