Auslander-Reiten quiver of type a and generalized quantum affine Schur-Weyl duality

The quiver Hecke algebra R can be also understood as a generalization of the affine Hecke algebra of type A in the context of the quantum affine Schur-Weyl duality by the results of Kang, Kashiwara and Kim. On the other hand, it is well known that the Auslander-Reiten (AR) quivers Γ_Q of finite simply-laced types have a deep relation with the positive roots systems of the corresponding types. In this paper, we present explicit combinatorial descriptions for the AR-quivers ΓQ of finite type A. Using the combinatorial descriptions, we can investigate relations between finite dimensional module categories over the quantum affine algebra (Formula Presented) and finite dimensional graded module categories over the quiver Hecke algebra R_An associated to A_n through the generalized quantum affine Schur-Weyl duality functor.