1 June 2015 Symmetric quiver Hecke algebras and R -matrices of quantum affine algebras, II
Seok-Jin Kang, Masaki Kashiwara, Myungho Kim
Duke Math. J. 164(8): 1549-1602 (1 June 2015). DOI: 10.1215/00127094-3119632


Let g be an untwisted affine Kac–Moody algebra of type A n ( 1 ) ( n 1 ) or D n ( 1 ) ( n 4 ), and let g 0 be the underlying finite-dimensional simple Lie subalgebra of g . For each Dynkin quiver Q of type g 0 , Hernandez and Leclerc introduced a tensor subcategory C Q of the category of finite-dimensional integrable U ' q ( g ) -modules and proved that the Grothendieck ring of C Q is isomorphic to C [ N ] , the coordinate ring of the unipotent group N associated with g 0 . We apply the generalized quantum affine Schur–Weyl duality to construct an exact functor F from the category of finite-dimensional graded R -modules to the category C Q , where R denotes the symmetric quiver Hecke algebra associated to g 0 . We prove that the homomorphism induced by the functor F coincides with the homomorphism of Hernandez and Leclerc and show that the functor F sends the simple modules to the simple modules.


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Seok-Jin Kang. Masaki Kashiwara. Myungho Kim. "Symmetric quiver Hecke algebras and R -matrices of quantum affine algebras, II." Duke Math. J. 164 (8) 1549 - 1602, 1 June 2015. https://doi.org/10.1215/00127094-3119632


Received: 2 August 2013; Revised: 11 July 2014; Published: 1 June 2015
First available in Project Euclid: 28 May 2015

zbMATH: 1323.81046
MathSciNet: MR3352041
Digital Object Identifier: 10.1215/00127094-3119632

Primary: 81R50
Secondary: 16G , 16T25 , 17B37

Keywords: quantum affine algebra , quantum group , quiver Hecke algebra

Rights: Copyright © 2015 Duke University Press


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Vol.164 • No. 8 • 1 June 2015
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