On uniform admissibility of unitary and smooth representations

Uriya A. First, Thomas Rüd

Research output: Contribution to journalArticlepeer-review

Abstract

Let G be a locally compact totally disconnected topological group. Under a necessary mild assumption, we show that the irreducible unitary representations of G are uniformly admissible if and only if the irreducible smooth representations of G are uniformly admissible. An analogous result for *-algebras is also established. We further show that the property of having uniformly admissible irreducible smooth representations is inherited by finite-index subgroups and overgroups of G.

Original languageEnglish
Pages (from-to)169-179
Number of pages11
JournalArchiv der Mathematik
Volume112
Issue number2
DOIs
StatePublished - 4 Feb 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

Keywords

  • Admissible representation
  • Locally compact group
  • Smooth representation
  • Unitary representation
  • p-adic reductive group

ASJC Scopus subject areas

  • Mathematics (all)

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