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Archiv der Mathematik

, Volume 112, Issue 2, pp 169–179 | Cite as

On uniform admissibility of unitary and smooth representations

  • Uriya A. FirstEmail author
  • Thomas Rüd
Article

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.

Keywords

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

Mathematics Subject Classification

22D10 22D12 

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Notes

Acknowledgements

We thank Maarten Solleveld for encouraging us to publish this note and the anonymous referee for suggesting to include Theorem 2.6.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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