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.
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- Auslander-Reiten quiver
- Generalized quantum affine Schur-Weyl duality
- Quiver Hecke algebra