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arXiv · 1803.01538

Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality

Ryo Fujita
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Abstract

For a Dynkin quiver $Q$ of type ADE and a sum $β$ 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-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 quiver $Q$ of dimension vector $β$. 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 R-matrices for any quiver $Q$ of type ADE.

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Ryo Fujita. 2019-11-28. Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality. https://doi.org/10.1093/imrn%2Frny226

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