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2017年10月31日

Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types

  • Ryo Fujita

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 of finite-dimensional modules is identified with a block of
Hernandez-Leclerc's monoidal category $\mathcal{C}_{Q}$ of modules over the
quantum loop algebra via Nakajima's homomorphism. As an application, we show
that Kang-Kashiwara-Kim's generalized quantum affine Schur-Weyl duality functor
gives an equivalence between the category of finite-dimensional modules of the
quiver Hecke algebra associated to $Q$ and Hernandez-Leclerc's category
$\mathcal{C}_{Q}$, assuming the simpleness of poles of normalized R-matrices
for type E.

リンク情報
arXiv
http://arxiv.org/abs/arXiv:1710.11288
Arxiv Url
http://arxiv.org/abs/1710.11288v1
Arxiv Url
http://arxiv.org/pdf/1710.11288v1 本文へのリンクあり

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