On Representations of Reductive $p$--adic Groups over $\mathbb{Q}$--algebras

Abstract

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb{Q}$--algebra. We prove some fundamental results in these settings, and as an example we give a classification of admissible unramified irreducible representations proving by reduction to the complex case that if the space of $K$--invariants is finite dimensional in an irreducible smooth unramified representation that the representation is admissible.

In v.2 we updated references and the introduction

References in corpus (2)

• On interactions between harmonic analysis and the theory of automorphic forms
• Representations of a $p$-adic group in characteristic $p$