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

Abstract

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-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 $\beta$. 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.

arXiv comment28 pages, v2: minor modifications, v3: final version

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Cited by in corpus (12)

• Monoidal categorification and quantum affine algebras
• Isomorphisms among quantum Grothendieck rings and propagation of positivity
• Categorical relations between Langlands dual quantum affine algebras: Exceptional cases
• Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types
• Graded quiver varieties and singularities of normalized R-matrices for fundamental modules
• Simplicity of tensor products of Kirillov--Reshetikhin modules: nonexceptional affine and G types
• Equivalence between module categories over quiver Hecke algebras and Hernandez-Leclerc's categories in general types
• A functor for constructing $R$-matrices in the category $\mathcal{O}$ of Borel quantum loop algebras
• Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras
• Braid group action on the module category of quantum affine algebras
• Inflations for representations of shifted quantum affine algebras
• PBW theoretic approach to the module category of quantum affine algebras