Geometric Realization of Dynkin Quiver Type Quantum Affine Schur-Weyl Duality
Geometric Realization of Dynkin Quiver Type Quantum Affine Schur-Weyl Duality
复制标题
Dynkin Quiver型量子仿射Schur-Weyl对偶性的几何实现
DOI：
10.1093/imrn/rny226
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发表时间：
2018
影响因子：
1
通讯作者：
Fujita Ryo
中科院分区：
文献类型：
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作者：
Fujita Ryo
对于Dynkin型和单根和，我们模仿Ginzburg-Reshetikhin-Vasserot的量子仿射Schur-Weyl对偶的几何实现，通过等变理论在量子环代数和相应类型的quiver Hecke代数上构造了一个双模。我们的构造是基于某种分级颤振簇与颤振维向量的表示空间之间的Hernandez-Leclerc同构。我们用Kang-Kashiwara-Kim的广义量子仿射Schur-Weyl对偶函子识别了由双模导出的函子。作为一个副产品，我们验证了Kang-Kashiwara-Kim关于任何微振型归一化矩阵的某些极点的简单性的猜想。
For a Dynkin quiverof typeand a sumof simple roots, we construct a bimodule over the quantum loop algebra and the quiver Hecke algebra of the corresponding type via equivariant-theory, imitating Ginzburg–Reshetikhin–Vasserot’s geometric realization of the quantum affine Schur–Weyl duality. Our construction is based on Hernandez–Leclerc’s isomorphism between a certain graded quiver variety and the space of representations of the quiverof dimension vector. We identify the functor induced from our bimodule with Kang–Kashiwara–Kim’s generalized quantum affine Schur–Weyl duality functor. As a by-product, we verify a conjecture by Kang–Kashiwara–Kim on the simpleness of some poles of normalized-matrices for any quiverof type.