Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cluster algebra structure on the finite dimensional representations of
  $U_q(\widehat{A_{3}})$ for $l$=2   In this paper, we prove one case of the conjecture given by Hernandez and
Leclerc\cite{HL0}. Specifically, we give a cluster algebra structure on the
Grothendieck ring of a full subcategory of the finite dimensional
representations of a simply-laced quantum affine algebra $U_q(\widehat{\g})$.
In the procedure, we also give a specific description of compatible subsets of
type $E_{6}$. As a conclusion, for every exchange relation of cluster algebra
there exists a exact sequence of the full subcategory corresponding to it.

27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex