Symmetric quiver Hecke algebras and R-matrices of quantum affine algebras

Let J be a set of pairs consisting of good -modules and invertible elements in the base field . The distribution of poles of normalized R-matrices yields Khovanov-Lauda-Rouquier algebras for each . We define a functor from the category of graded -modules to the category of -modules. The functor sends convolution products of finite-dimensional graded -modules to tensor products of finite-dimensional -modules. It is exact if is of finite type A, D, E. If is the fundamental representation of of weight and , then is the Khovanov-Lauda-Rouquier algebra of type . The corresponding functor sends a finite-dimensional graded -module to a module in , where is the category of finite-dimensional integrable -modules M such that every composition factor of M appears as a composition factor of a tensor product of modules of the form . Focusing on this case, we obtain an abelian rigid graded tensor category by localizing the category of finite-dimensional graded -modules. The functor factors through . Moreover, the Grothendieck ring of the category is isomorphic to the Grothendieck ring of at .