Twisted Coxeter elements and folded AR-quivers via Dynkin diagram\n automorphisms: I

2016/05/31 by Se‐jin Oh, Oh, Se-jin, UhiRinn Suh +1
Mathematics · Physics and Astronomy · #05E10 #16T30 #17B37 #81R50 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1606.00076

openalex publication_date 2016/05/31 · openalex created_date 2022/09/10 · openalex updated_date 2026/07/28

Abstract

We introduce and study the twisted adapted r-cluster point and its\ncombinatorial Auslander-Reiten quivers, called twisted AR-quivers and folded\nAR-quivers, of type A_2n+1 which are closely related to twisted Coxeter\nelements and the non-trivial Dynkin diagram automorphism. As applications of\nthe study, we prove that folded AR-quivers encode crucial information on the\nrepresentation theory of quantum affine algebra U_q'(B⁽¹⁾_n+1) such as\nDorey's rule and denominator formulas.\n

Citations

• 2-Kac-Moody algebras

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