Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Continuous Spectrum in Discrete Series Branching Laws   If $G$ is a reductive Lie group of Harish-Chandra class, $H$ is a symmetric
subgroup, and $\pi$ is a discrete series representation of $G$, the authors
give a condition on the pair $(G,H)$ which guarantees that the direct integral
decomposition of $\pi|_H$ contains each irreducible representation of $H$ with
finite multiplicity. In addition, if $G$ is a reductive Lie group of
Harish-Chandra class, and $H\subset G$ is a closed, reductive subgroup of
Harish-Chandra class, the authors show that the multiplicity function in the
direct integral decomposition of $\pi|_H$ is constant along `continuous
parameters'. In obtaining these results, the authors develop a new technique
for studying multiplicities in the restriction $\pi|_H$ via convolution with
Harish-Chandra characters. This technique has the advantage of being useful for
studying the continuous spectrum as well as the discrete spectrum.

31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat