Discrete series of simple Lie groups with admissible restriction to a $SL_2(\mathbb R)$

Abstract

In this note we determine the irreducible square integrable representations of a simple group which admits an admissible restriction to a subgroup $H$ locally isomorphic to $SL_2(\mathbb R).$ We show such representation is holomorphic and we determine the essentially unique $H$ with this property as well as multiplicity formulae.