Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types
| Autor: | Naoi, Katsuyuki |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Advances in Mathematics 389 (2021) 107916 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2021.107916 |
| Popis: | 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. Comment: 40 pages, 1 figure, changed the title in version 3; changed the proof Proposition 5.2.5 completely, corrected unclear expressions and typos in version 2 |
| Databáze: | arXiv |
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