Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The quantum $\mathfrak{sl}(n,\mathbb{C})$ representation theory and its
  applications   In this paper, we study the quantum $\mathfrak{sl}(n)$ representation
category using the web space. Specially, we extend $\mathfrak{sl}(n)$ web space
for $n\ge 4$ as generalized Temperley-Lieb algebras. As an application of our
study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one
variable polynomial can be computed by a linear expansion with respect to a
presentation of the quantum representation category of $\mathfrak{sl}(n)$.
Moreover, we correct the false conjecture \cite{PS:superiod} given by Chbili,
which addresses the relation between some link polynomials of a periodic link
and its factor link such as Alexander polynomial $(n = 0)$ and Jones polynomial
$(n = 2)$ and prove the corrected conjecture not only for HOMFLY polynomial but
also for the colored HOMFLY polynomial specialized to a one variable
polynomial.

18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol