# Types and unitary representations of reductive p-adic groups

Ciubotaru, D

1 February 2018

## Journal:

Inventiones Mathematicae

## Last Updated:

2020-11-09T19:21:00.997+00:00

1

213

## DOI:

10.1007/s00222-018-0790-4

237-269

## abstract:

We prove that for every Bushnell-Kutzko type that satisfies a certain rigidity assumption, the equivalence of categories between the corresponding Bernstein component and the category of modules for the Hecke algebra of the type induces a bijection between irreducible unitary representations in the two categories. Moreover, we show that every irreducible smooth G-representation contains a rigid type. This is a generalization of the unitarity criterion of Barbasch and Moy for representations with Iwahori fixed vectors.

708979

Submitted

Journal Article