Representations of non quasi-split unramified U(4) over a p-adic field I:Representations of non-integral level

TL;DR

This paper classifies irreducible smooth representations of a specific non quasi-split unramified unitary group over a p-adic field at non-integral levels, using Hecke algebra techniques.

Contribution

It provides the first classification of non-integral level representations for this particular group using Hecke algebra methods.

Findings

Classification of non-integral level representations achieved

Hecke algebra approach successfully applied to non quasi-split groups

Enhanced understanding of representation theory for unramified unitary groups

Abstract

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the non quasi-split unramified unitary group in four variables defined over F_0. In this paper, we give a classification of the irreducible smooth representations of G of non-integral level using the Hecke algebraic method developed by Howe and Moy.