Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality
Abstract
For a Dynkin quiver of type ADE and a sum 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 of 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 R-matrices for any quiver of type ADE.
Keywords
Cite
@article{arxiv.1803.01538,
title = {Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality},
author = {Ryo Fujita},
journal= {arXiv preprint arXiv:1803.01538},
year = {2019}
}
Comments
28 pages, v2: minor modifications, v3: final version