Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum groups and functional relations for arbitrary rank   The quantum integrable systems associated with the quantum loop algebras
$\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The
factorized form of the transfer operators related to the infinite dimensional
evaluation representations is found and the determinant form of the transfer
operators related to the finite dimensional evaluation representations is
obtained. The master $TQ$- and $TT$-relations are derived. The operatorial $T$-
and $Q$-systems are found. The nested Bethe equations are obtained.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci