R-matrices for quantum affine algebras and Khovanov-Lauda-Rouquier algebras, I

Abstract

Let us consider a finite set of pairs consisting of good $U_q^{\prime }(g)$-modules and invertible elements. The distribution of poles of normalized R-matrices yields Khovanov-Lauda-Rouquier algebras We define a functor from the category of finite-dimensional modules over the KLR algebra to the category of finite-dimensional $U_q^{\prime }(g)$-modules. We show that the functor sends convolution products to tensor products and is exact if the KLR albera is of type A, D, E.

19 pages, this paper is merged to arXiv:1304.0323

References in corpus (1)

• 2-Kac-Moody algebras