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

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.