Metaplectic Tori over Local Fields

TL;DR

This paper extends the Langlands parameterization of smooth irreducible representations from tori over local fields to their central extensions, which are relevant in nonlinear covers of reductive groups.

Contribution

It introduces a new parameterization framework for central extensions of tori over local fields, expanding the Langlands program to nonlinear covers.

Findings

Extended the Langlands parameterization to central extensions of tori

Connected nonlinear covers of reductive groups with representation theory

Provided a new perspective on class field theory applications

Abstract

Smooth irreducible representations of tori over local fields have been parameterized by Langlands, using class field theory and Galois cohomology. This paper extends this parameterization to central extensions of such tori, which arise naturally in the setting of nonlinear covers of reductive groups.