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    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 Ξ“Q\Gamma^Q of finite type DD. Then we can investigate the categories of finite dimensional representations over the quantum affine algebra Uqβ€²(Dn+1(i))U_q'(D^{(i)}_{n+1}) (i=1,2)(i=1,2) and the quiver Hecke algebra RDn+1R_{D_{n+1}} associated to Dn+1D_{n+1} (nβ‰₯3)(n \ge 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(R_{D_{n+1}}) and prove an interesting difference between multiplicity free positive roots and multiplicity non-free positive roots.Comment: We added the result on relationship between denominator formulas and AR-quive
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