Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $S$-matrix in permutation orbifolds   For a fixed positive integer $k$, any element $g$ of the permutation group
$S_{k}$ acts on the tensor product vertex operator algebra $V^{\otimes k}$ in
the obvious way. In this paper, we determine the $S$-matrix of
$\left(V^{\otimes k}\right)^{G}$ if $G=\left\langle g\right\rangle $ is the
cyclic group generated by $g=\left(1,\ 2,\cdots,k\right).$

17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ