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arXiv · 2101.03573

Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types

Katsuyuki Naoi
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Abstract

We prove in full generality that the generalized quantum affine Schur-Weyl duality functor, introduced by Kang-Kashiwara-Kim, gives an equivalence between the category of finite-dimensional modules over a quiver Hecke algebra and a certain full subcategory of finite-dimensional modules over a quantum affine algebra which is a generalization of the Hernandez-Leclerc's category $\mathcal{C}_Q$. This was previously proved in untwisted $ADE$ types by Fujita using the geometry of quiver varieties, which is not applicable in general. Our proof is purely algebraic, and so can be extended uniformly to general types.

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BibTeXRIS

Katsuyuki Naoi. 2021-01-10. Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types. https://doi.org/10.1016/j.aim.2021.107916

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