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

2019/05/06 by Goran Muić, Muić, Goran
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.1905.01949

In v.2 we updated references and the introduction

openalex publication_date 2019/05/06 · arxiv created 2019/05/10 · arxiv updated 2019/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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