Duke Mathematical Journal
- Duke Math. J.
- Volume 164, Number 8 (2015), 1549-1602.
Symmetric quiver Hecke algebras and -matrices of quantum affine algebras, II
Let be an untwisted affine Kac–Moody algebra of type ( ) or ( ), and let be the underlying finite-dimensional simple Lie subalgebra of . For each Dynkin quiver of type , Hernandez and Leclerc introduced a tensor subcategory of the category of finite-dimensional integrable -modules and proved that the Grothendieck ring of is isomorphic to , the coordinate ring of the unipotent group associated with . We apply the generalized quantum affine Schur–Weyl duality to construct an exact functor from the category of finite-dimensional graded -modules to the category , where denotes the symmetric quiver Hecke algebra associated to . We prove that the homomorphism induced by the functor coincides with the homomorphism of Hernandez and Leclerc and show that the functor sends the simple modules to the simple modules.
Duke Math. J., Volume 164, Number 8 (2015), 1549-1602.
Received: 2 August 2013
Revised: 11 July 2014
First available in Project Euclid: 28 May 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]
Secondary: 16G 16T25: Yang-Baxter equations 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho. Symmetric quiver Hecke algebras and $R$ -matrices of quantum affine algebras, II. Duke Math. J. 164 (2015), no. 8, 1549--1602. doi:10.1215/00127094-3119632. https://projecteuclid.org/euclid.dmj/1432817758