Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local action of the symmetric group and the twisted Yang-Baxter relation   The generalization of the the Yang-Baxter relation is proposed. In this
generalization the spectral parameters of the particles change after the
scattering. The corresponding algebraic structures are discussed. The
corresponding action of the symmetric group is studied. The most interesting
examples of such action are connected with factorization of matrix polynomials
and matrix $theta$-functions. The generalization of the star-triangle relation
is also proposed.

25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int