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

Abstract

We first provide an explicit combinatorial description of the Auslander-Reiten quiver Gamma(Q) of finite type D. Then we can investigate the categories of finite dimensional representations over the quantum affine algebra U-q'(D-n+1((i))) (i = 1,2) and the quiver Hecke algebra RDn+1, associated to Dn+1 (n >= 3), by using the combinatorial description and the generalized quantum affine Schur-Weyl duality functor. As applications, we can prove that Dorey's rule holds for the category Rep(RDn+1) and prove an interesting difference between multiplicity free positive roots and multiplicity non-free positive roots. (C) 2016 Elsevier Inc. All rights reserved.