Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Star product induced from coherent states on $L^2(S^n)$, $n = 2, 3, 5$   We consider the bounded linear operators with domain in the Hilbert space
$L^2(S^n)$, $n=2,3,5$ and describe its symbolic calculus defined by the Berezin
quantization. In particular, we derive an explicit formula for the composition
of Berezin's symbols and thus a noncommutative invariant star product, which in
turn is invariant under the action of the group $SU(2)$, $SU(2)\times SU(2)$
and $SU(4)$ on $\mathbb C^2$ , $\mathbb C^4$ and $\mathbb C^8$ respectively.

15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol