Spherical pairs over close local fields

Avraham Aizenbud*, Nir Avni, Dmitry Gourevitch

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Extending results of [Kaz86] to the relative case, we relate harmonic analysis over some spherical spaces G.(F)/H.(F), where F is a field of positive characteristic, to harmonic analysis over the spherical spaces G.(E)=H.(E), where E is a suitably chosen field of characteristic 0. We apply our results to show that the pair .(GLnC1.F ); GL n.(F)) is a strong Gelfand pair for all local fields of arbitrary characteristic, and that the pair .GL nCk.(F); GL n.(F)̃GLk.(F)) is a Gelfand pair for local fields of any characteristic different from 2. We also give a criterion for finite generation of the space of K-invariant compactly supported functions on G.E/=H.E/ as a module over the Hecke algebra.

Original languageEnglish (US)
Pages (from-to)929-962
Number of pages34
JournalCommentarii Mathematici Helvetici
Volume87
Issue number4
DOIs
Publication statusPublished - Nov 1 2012

    Fingerprint

Keywords

  • Gelfand pair
  • Multiplicity
  • Reductive group
  • Uniqueness of linear periods

ASJC Scopus subject areas

  • Mathematics(all)

Cite this