Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applications of the Capelli identities in physics and representation
  theory   Capelli identities are shown to facilitate the construction of
representations of various Heisenberg algebras that arise in many-particle
quantum mechanics and the construction of holomorphic representations of many
Lie algebras by Vector Coherent State methods. We consider the original Capelli
identity and its generalizations by Turnbull and by Howe and Umeda.

23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th