# Restriction of representations of metaplectic $GL_{2}(F)$ to tori

## TL;DR

This paper investigates how irreducible admissible genuine representations of the metaplectic cover of $GL_2(F)$ behave when restricted to the inverse images of maximal tori, revealing new structural insights.

## Contribution

It provides a detailed analysis of the restriction of genuine representations of the metaplectic $GL_2(F)$ to maximal tori, a previously less understood aspect.

## Key findings

- Characterization of restrictions to tori
- Identification of conditions for irreducibility
- Insights into representation structure

## Abstract

Let $F$ be a non-Archimedean local field. We study the restriction of an irreducible admissible genuine representations of the two fold metaplectic cover $\widetilde{GL}_{2}(F)$ of $GL_{2}(F)$ to the inverse image in $\widetilde{GL}_{2}(F)$ of a maximal torus in $GL_{2}(F)$.