Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Set theoretic Yang-Baxter & reflection equations and quantum group
  symmetries   Connections between set-theoretic Yang-Baxter and reflection equations and
quantum integrable systems are investigated. We show that set-theoretic
$R$-matrices are expressed as twists of known solutions. We then focus on
reflection and twisted algebras and we derive the associated defining algebra
relations for $R$-matrices being Baxterized solutions of the $A$-type Hecke
algebra ${\cal H}_N(q=1)$. We show in the case of the reflection algebra that
there exists a ``boundary'' finite sub-algebra for some special choice of
``boundary'' elements of the $B$-type Hecke algebra ${\cal B}_N(q=1, Q)$. We
also show the key proposition that the associated double row transfer matrix is
essentially expressed in terms of the elements of the $B$-type Hecke algebra.
This is one of the fundamental results of this investigation together with the
proof of the duality between the boundary finite subalgebra and the $B$-type
Hecke algebra. These are universal statements that largely generalize previous
relevant findings, and also allow the investigation of the symmetries of the
double row transfer matrix.

25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int