Bounds on multiplicities of spherical spaces over finite fields

Avraham Aizenbud, Nir Avni*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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
Issue number9
StatePublished - Sep 2019


  • Representations of groups of Lie type

ASJC Scopus subject areas

  • Algebra and Number Theory


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