English

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

Number Theory 2019-05-13 v2 Representation Theory

Abstract

In this paper we study certain category of smooth modules for reductive pp--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a Q\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 KK--invariants is finite dimensional in an irreducible smooth unramified representation that the representation is admissible.

Keywords

Cite

@article{arxiv.1905.01949,
  title  = {On Representations of Reductive $p$--adic Groups over $\mathbb Q$--algebras},
  author = {Goran Muić},
  journal= {arXiv preprint arXiv:1905.01949},
  year   = {2019}
}

Comments

In v.2 we updated references and the introduction

R2 v1 2026-06-23T08:57:57.655Z