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 ΓQ of finite type D. Then we can investigate the categories of finite dimensional representations over the quantum affine algebra Uq′(Dn+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.