A note on the admissibility of smooth simple $RG$-modules

Abstract

Let G be a p-adic reductive group and R be a noetherian Jacobson algebra over the ring Zl of l-adic integers with l ≠ p. In this note, we show that every smooth irreducible R-linear representation of G is admissible using the finiteness result of Dat, Helm, Kurinczuk and Moss for Hecke algebras over R. Mathematics Subject Classification (2020) – Primary 22E50; Secondary 11F70, 20C08.