Classification of irreducible representations of metaplectic covers of the general linear group over a non-archimedean local field

TL;DR

This paper extends the Bernstein--Zelevinsky classification of irreducible representations from linear groups to metaplectic covers of $GL_n(F)$ over non-archimedean local fields, providing a new framework for understanding these representations.

Contribution

It introduces a classification scheme for irreducible representations of metaplectic covers of $GL_n(F)$, analogous to the classical theory for linear groups.

Findings

Established a classification for metaplectic covers of $GL_n(F)$

Extended Bernstein--Zelevinsky theory to non-linear covers

Provided foundational results for future representation theory research

Abstract

Let $F$ be a non-archimedean local field. The classification of the irreducible representations of $GL_n(F)$, $n\ge0$ in terms of supercuspidal representations is one of the highlights of the Bernstein--Zelevinsky theory. We give an analogous classification for metaplectic coverings of $GL_n(F)$, $n\ge0$.