Restriction of representations of metaplectic $G{L}_2(F)$ to tori

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 $G{L}_2(F)$ to the inverse image in ${\widetilde{GL}}_2(F)$ of a maximal torus in $G{L}_2(F)$.