Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the simplicity of the tensor product of two simple modules of quantum
  affine algebras   Lapid and M\'{i}nguez gave a criterion of the irreducibility of the parabolic
induction $\sigma \times \pi$, where $\sigma$ is a ladder representation and
$\pi$ is an arbitrary irreducible representation of the general linear group
over a non-archimedean field. Through quantum affine Schur-Weyl duality, when
$k$ is large enough, this gives a criterion of the irreducibility of the tensor
product of a snake module $L(M)$ and any simple module $L(N)$ of the quantum
affine algebra $U_q(\widehat{\mathfrak{sl}_k})$.
  The goal of this paper is to add conditions to their criterion such that it
works for any $k \geq 1$. We prove the criterion in the case that $L(M)$,
$L(N)$ are snake modules or $M=Y_{1,s}$ for some $s \in \mathbb{Z}$, $L(N)$ is
any simple module. We also defined a similar criterion in terms of two tableaux
and show that for any $k \geq 1$, two ladders in the Grassmannian cluster
algebra $\mathbb{C}[\mathrm{Gr}(k,n, \sim)]$ are compatible if and only if the
corresponding tableaux satisfy the criterion. This generalizes Leclerc and
Zelevinsky's result that two Pl\"{u}cker coordinates are compatible if and only
if they are weakly separated.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an