2014/05/14 by Se‐jin Oh, Oh, Se-jin
Mathematics · #05E10 #16T30 #17B37 #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.1405.3336
openalex publication_date 2014/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The quiver Hecke algebra R can be also understood as a generalization of the affine Hecke algebra of type A in the context of the quantum affine Schur-Weyl duality by the results of Kang, Kashiwara and Kim. On the other hand, it is well-known that the Auslander-Reiten(AR) quivers ΓQ of finite simply-laced types have a deep relation with the positive roots systems of the corresponding types. In this paper, we present explicit combinatorial descriptions for the AR-quivers ΓQ of finite type A. Using the combinatorial descriptions, we can investigate relations between finite dimensional module categories over the quantum affine algebra U'q(An(i)) (i=1,2) and finite dimensional graded module categories over the quiver Hecke algebra RAn associated to An through the generalized quantum affine Schur-Weyl duality functor.