Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Braid group approach to the derivation of universal \v{R} matrices   A new method for deriving universal \v{R} matrices from braid group
representation is discussed. In this case, universal \v{R} operators can be
defined and expressed in terms of products of braid group generators. The
advantage of this method is that matrix elements of \v{R} are rank independent,
and leaves multiplicity problem concerning coproducts of the corresponding
quantum groups untouched. As examples, \v{R} matrix elements of $[1]\times
  [1]$, $[2]\times [2]$, $[1^{2}]\times [1^{2}]$, and $[21]\times [21]$ with
multiplicity two for $A_{n}$, and $[1]\times [1]$ for $B_{n}$,
  $C_{n}$, and $D_{n}$ type quantum groups, which are related to Hecke algebra
and Birman-Wenzl algebra, respectively, are derived by using this method.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio