English

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

Representation Theory 2016-07-25 v2 Combinatorics Quantum Algebra

Abstract

As a continuation of the previous paper, we find a combinatorial interpretation of Dorey's rule for type CnC_n via twisted Auslander-Reiten quivers (AR-quivers) of type Dn+1D_{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 Uq(Cn(1))U_q'(C_n^{(1)}) such as denominator formulas. In addition, unlike twisted adapted classes of type A2n1A_{2n-1} in the previous paper, we show twisted AR-quivers of type Dn+1D_{n+1} consist of the cluster point called twisted adapted cluster point. Hence, by introducing new combinatorial objects called twisted Dynkin quivers of type Dn+1D_{n+1}, we give one to one correspondences between twisted Coxeter elements, twisted adapted classes and twisted AR-quivers.

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Cite

@article{arxiv.1606.00102,
  title  = {Twisted Coxeter elements and Folded AR-quivers via Dynkin diagram automorphisms:II},
  author = {Se-Jin Oh and UhiRinn Suh},
  journal= {arXiv preprint arXiv:1606.00102},
  year   = {2016}
}

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53pages