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arXiv · 1904.01264

Cluster algebra structures on module categories over quantum affine algebras

Masaki Kashiwara·Myungho Kim·Se-jin Oh·Euiyong Park
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Abstract

We study monoidal categorifications of certain monoidal subcategories $\mathcal{C}_J$ of finite-dimensional modules over quantum affine algebras, whose cluster algebra structures coincide and arise from the category of finite-dimensional modules over quiver Hecke algebra of type A${}_\infty$. In particular, when the quantum affine algebra is of type A or B, the subcategory coincides with the monoidal category $\mathcal{C}_{\mathfrak{g}}^0$ introduced by Hernandez-Leclerc. As a consequence, the modules corresponding to cluster monomials are real simple modules over quantum affine algebras.

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BibTeXRIS

Masaki Kashiwara, Myungho Kim, Se-jin Oh, Euiyong Park. 2019-04-02. Cluster algebra structures on module categories over quantum affine algebras. https://arxiv.org/abs/1904.01264

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