# Discrete decomposability of the restriction of $A_q(\lambda)$ with respect to reductive subgroups II: Micro-local analysis and asymptotic $K$-support

### Abstract

Let $’ \subset G$ be real reductive Lie groups. This paper offers a criterion on the triplet $(G,G’,\pi)$ that the irreducible unitary representation $\pi$ of $G$ splits into a discrete sum o irreducible unitary representaitons of a subgroup $G’$ when restricted to $G’$, each of finite multiplicity. Furthermore, we shall give an upper estimates of the multiplicity o an irreducible unitary representation of $G’$ occurring in $\pi\mid_{G’}$.

## Authors

Toshiyuki Kobayashi