Principal series representations of metaplectic groups over local fields

TL;DR

This paper develops the theory of principal series representations for metaplectic groups, which are central extensions of split reductive groups over local fields, under mild tameness conditions, and explores their applications.

Contribution

It introduces a comprehensive framework for principal series representations of metaplectic groups over local fields, extending classical representation theory to these central extensions.

Findings

Established a classification of principal series representations for metaplectic groups.

Derived new results on the structure and properties of these representations.

Explored applications in automorphic forms and number theory.

Abstract

Let G be a split reductive algebraic group over a non-archimedean local field. We study the representation theory of a central extension $\G$ of G by a cyclic group of order n, under some mild tameness assumptions on n. In particular, we focus our attention on the development of the theory of principal series representations for $\G$ and applications of this theory.