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

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• 作者：Se-jin Oh¹ ; ^{sejin092@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 05E10 ; 16T30 ; 17B37 ; secondary ; 81R50
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 August 2016
• 年：2016
• 卷：460
• 期：Complete
• 页码：203-252
• 全文大小：781 K

文摘

We first provide an explicit combinatorial description of the Auslander–Reiten quiver Γ_Q${\mathrm{\Gamma }}_Q$ of finite type D  . Then we can investigate the categories of finite dimensional representations over the quantum affine algebra $U_q^{\prime }(D_{n+1}^{(i)})$(i=1,2)$(i=1,2)$ and the quiver Hecke algebra R_Dn+1$R_{D_{n+1}}$ associated to D_n+1$D_{n+1}$(n≥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_Dn+1)$\mathrm{Rep}(R_{D_{n+1}})$ and prove an interesting difference between multiplicity free positive roots and multiplicity non-free positive roots.