On Uniform Admissibility of Unitary and Smooth Representations

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. We also show that the latter property is inherited by finite-index subgroups and overgroups of $G$.

7 pages; comments are welcome

References in corpus (1)

• The Ramanujan Property for Simplicial Complexes

Cited by in corpus (2)

• Probing holography in $p$-adic CFT
• Quantum sets and Gelfand spectra (Ortho-sets and Gelfand spectra)