On uniform admissibility of unitary and smooth representations

Uriya A. First; Thomas Rüd

doi:10.1007/s00013-018-1257-y

On uniform admissibility of unitary and smooth representations

Uriya A. First, Thomas Rüd

Department of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	169-179
Number of pages	11
Journal	Archiv der Mathematik
Volume	112
Issue number	2
DOIs	https://doi.org/10.1007/s00013-018-1257-y
State	Published - 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

General Mathematics

Access to Document

10.1007/s00013-018-1257-y

Cite this

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KW - Locally compact group

KW - Smooth representation

KW - Unitary representation

KW - p-adic reductive group

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On uniform admissibility of unitary and smooth representations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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