Representations of unramified U(2,2) over a p-adic field I: representations of non-integral level

TL;DR

This paper classifies irreducible smooth representations of the unramified U(2,2) group over a p-adic field at non-integral levels, extending the Hecke algebraic approach originally used for GSp(4).

Contribution

It provides a new classification of non-integral level representations for U(2,2) using Hecke algebra techniques.

Findings

Classification of non-integral level representations achieved

Extension of Moy's Hecke algebra method to U(2,2)

Framework for analyzing representations of p-adic unitary groups

Abstract

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the unramified unitary group U(2,2) 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 Allen Moy for GSp(4).