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

2014/06/17 by Se‐jin Oh, Oh, Se-jin
Mathematics · #16T30 #17B37 #5E10 #81R50 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1406.4555

openalex publication_date 2014/06/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We first provide an explicit combinatorial description of the\nAuslander-Reiten quiver \Γ^Q of finite type D. Then we can investigate\nthe categories of finite dimensional representations over the quantum affine\nalgebra U_q'(D⁽ⁱ⁾_n+1) (i=1,2) and the quiver Hecke algebra\nR_D_n+1 associated to D_n+1 (n \≥ 3), by using the combinatorial\ndescription and the generalized quantum affine Schur-Weyl duality functor. As\napplications, we can prove that Dorey's rule holds for the category\n Rep(R_D_n+1) and prove an interesting difference between multiplicity\nfree positive roots and multiplicity non-free positive roots.\n

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