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

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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'(D⁽ⁱ⁾ₙ₊₁) (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 (RDₙ₊₁) and prove an interesting difference between multiplicity free positive roots and multiplicity non-free positive roots.