Equivalence between module categories over quiver Hecke algebras and Hernandez?Leclerc's categories in general types
Equivalence between module categories over quiver Hecke algebras and Hernandez?Leclerc's categories in general types
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一般类型中的赫克代数和 Hernandez?Leclerc 范畴上的模块范畴之间的等价性
DOI：
10.1016/j.aim.2021.107916
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发表时间：
2021
影响因子：
1.7
通讯作者：
Naoi Katsuyuki
中科院分区：
文献类型：
--
作者：
川口良;Naoi Katsuyuki
我们证明了Kang-Kashiwara-Kim引入的广义量子仿射Schur-Weyl对偶函子给出了Hernan-Hecke代数上的有限维模范畴与量子仿射代数上的有限维模的某个满子范畴之间的等价性，量子仿射代数是Hernan-Leclerc范畴C Q的推广.这是以前证明了在untwisted ADE类型的藤田使用的几何学的numerous品种，这是不适用的一般。我们的证明是纯代数的，因此可以统一推广到一般类型。
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 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.