Branching of metaplectic representation of $Sp(2, \mathbb R)$ under its principal $SL(2, \mathbb R)$-subgroup

TL;DR

This paper investigates how the metaplectic representation of the symplectic group Sp(2, R) decomposes when restricted to its principal SL(2, R) subgroup, providing a complete decomposition analysis.

Contribution

It provides the first complete decomposition of the metaplectic representation of Sp(2, R) under its principal SL(2, R) subgroup.

Findings

Complete decomposition of the metaplectic representation obtained

Explicit branching rules derived for the subgroup

Advances understanding of representation theory of symplectic groups

Abstract

We study branching problem of the metaplectic representation of $Sp(2, \mathbb R)$ under its principle subgroup $SL(2, \mathbb R)$. We find the complete decomposition.