Local newforms for generic representations of unramified odd unitary groups and Fundamental Lemma

TL;DR

This paper develops the theory of local newforms for generic representations of unramified odd unitary groups and proves an analogue of the fundamental lemma for these groups.

Contribution

It introduces the concept of local newforms for these groups and establishes a fundamental lemma analogue, advancing the understanding of their representation theory.

Findings

Established the theory of local newforms for unramified odd unitary groups.

Proved an analogue of the fundamental lemma for these groups.

Enhanced the framework for studying representations of p-adic unitary groups.

Abstract

In this paper, we establish the theory of local newforms for irreducible tempered generic representations of unramified odd unitary groups over a non-archimedean local field. For the proof, we prove an analogue of the fundamental lemma for our compact groups.