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تسجيل مستخدم جديدGeometric realization of Dynkin quiver type quantum affine Schur-Weyl duality
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تأليف
Ryo Fujita
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For a Dynkin quiver $Q$ of type ADE and a sum $beta$ of simple roots, we construct a bimodule over the quantum loop algebra and the quiver Hecke algebra of the corresponding type via equivariant K-theory, imitating Ginzburg-Reshetikhin-Vasserots geometric realization of the quantum affine Schur-Weyl duality. Our construction is based on Hernandez-Leclercs isomorphism between a certain graded quiver variety and the space of representations of the quiver $Q$ of dimension vector $beta$. We identify the functor induced from our bimodule with Kang-Kashiwara-Kims 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 R-matrices for any quiver $Q$ of type ADE.
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For a Dynkin quiver $Q$ (of type ADE), we consider a central completion of the convolution algebra of the equivariant K-group of a certain Steinberg type graded quiver variety. We observe that it is affine quasi-hereditary and prove that its category
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