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- W4225939488 abstract "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 where both modules are snake modules or one of them is a fundamental module at an extremity node and the other is any simple module. We also defined a similar criterion in the Grassmannian cluster algebra $mathbb{C}[mathrm{Gr}(k,n, sim)]$, and show that for any $k geq 1$, two ladders 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." @default.
- W4225939488 created "2022-05-05" @default.
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- W4225939488 date "2022-03-31" @default.
- W4225939488 modified "2023-10-17" @default.
- W4225939488 title "On the simplicity of the tensor product of two simple modules of quantum affine algebras" @default.
- W4225939488 doi "https://doi.org/10.48550/arxiv.2203.17268" @default.
- W4225939488 hasPublicationYear "2022" @default.
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