Twisted Coxeter elements and Folded AR-quivers via Dynkin diagram automorphisms:II

2016/06/01 by Se-Jin Oh, Oh, Se-Jin, UhiRinn Suh +1
Mathematics · #05E10 #16T30 #17B37 #81R50 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1606.00102

openalex publication_date 2016/06/01 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28

Abstract

As a continuation of the previous paper, we find a combinatorial interpretation of Dorey's rule for type C_n via twisted Auslander-Reiten quivers (AR-quivers) of type D_n+1, which are combinatorial AR-quivers related to certain Dynkin diagram automorphisms. Combinatorial properties of twisted AR-quivers are useful to understand not only Dorey's rule but also other notions in the representation theory of the quantum affine algebra U_q'(C_n⁽¹⁾) such as denominator formulas. In addition, unlike twisted adapted classes of type A_2n-1 in the previous paper, we show twisted AR-quivers of type D_n+1 consist of the cluster point called twisted adapted cluster point. Hence, by introducing new combinatorial objects called twisted Dynkin quivers of type D_n+1, we give one to one correspondences between twisted Coxeter elements, twisted adapted classes and twisted AR-quivers.

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