Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Restriction to symmetric subgroups of unitary representations of rank
  one semisimple Lie groups   We consider the spherical complementary series of rank one Lie groups
$H_n=\SO_0(n, 1; \mathbb F)$ for $\mathbb F=\mathbb R, \mathbb C, \mathbb H$.
We prove that there exist finitely many discrete components in its restriction
under the subgroup $H_{n-1}=\SO_0(n-1, 1; \mathbb F)$. This is proved by
imbedding the complementary series into analytic continuation of holomorphic
discrete series of $G_n=SU(n, 1)$, $SU(n, 1)\times SU(n, 1)$ and $SU(2n, 2)$
and by the branching of holomorphic representations under the corresponding
subgroup
  $G_{n-1}$.

4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc