AUSLANDER-REITEN QUIVER OF TYPE A AND GENERALIZED QUANTUM AFFINE SCHUR-WEYL DUALITY

Abstract

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 Gamma(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 Gamma(Q) of finite type A. Using the combinatorial descriptions, we can investigate relations between finite dimensional module categories over the quantum affine algebra U-q'(A(n)((i))) (i = 1, 2) 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.