Branching laws for the metaplectic cover of ${\rm GL}_{2}$

Abstract: Let $F$ be a non-Archimedian local field of characteristic zero and $E/F$ a quadratic extension. The aim of the present article is to study the multiplicity of an irreducible admissible representation of ${\rm GL}_2(F)$ occurring in an irreducible admissible genuine representation of non-trivial two fold covering $\widetilde{{\rm GL}}_2(E)$ of ${\rm GL}_2(E)$.