Branching laws for the metaplectic cover of $\mathrm{GL}_2$

Shiv Prakash Patel

Vol. 291 (2017), No. 2, 461–484

DOI: 10.2140/pjm.2017.291.461

Abstract

Let $F$ be a nonarchimedean local field of characteristic zero and $E∕F$ be a quadratic extension. The aim of this article is to study the multiplicity of an irreducible admissible representation of ${GL}_2\left(F\right)$ occurring in an irreducible admissible genuine representation of the nontrivial two-fold covering ${\widetilde{GL}}_2\left(E\right)$ of ${GL}_2\left(E\right)$.

Keywords

metaplectic group, branching laws

Mathematical Subject Classification 2010

Primary: 22E35

Secondary: 22E50

Milestones

Received: 21 September 2016

Revised: 9 May 2017

Accepted: 9 May 2017

Published: 14 September 2017