R-matrices for quantum affine algebras and Khovanov-Lauda-Rouquier   algebras, I
  Let us consider a finite set of pairs consisting of good $U'_q(g)$-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 $U_q'(g)$-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. 
Seok-Jin Kang, Masaki Kashiwara, Myungho Kim
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