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Let us consider a finite set of pairs consisting of good $U'_q(g)$-modulesand invertible elements. The distribution of poles of normalized R-matricesyields Khovanov-Lauda-Rouquier algebras We define a functor from the categoryof finite-dimensional modules over the KLR algebra to the category offinite-dimensional $U_q'(g)$-modules. We show that the functor sendsconvolution products to tensor products and is exact if the KLR albera is oftype A, D, E.

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