Kirillov’s orbit method: The case of discrete series representations

Abstract

Let $\pi$ be a discrete series representation of a real reductive Lie group $G\text{'}$, and let $G$ be a reductive subgroup of $G\text{'}$. In this paper, we give a geometric expression of the $G$-multiplicities in $\pi {|}_G$ when the representation $\pi$ is $G$-admissible.