Twisted Coxeter elements and Folded AR-quivers via Dynkin diagram automorphisms:II
Abstract
As a continuation of the previous paper, we find a combinatorial interpretation of Dorey's rule for type via twisted Auslander-Reiten quivers (AR-quivers) of type , 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 such as denominator formulas. In addition, unlike twisted adapted classes of type in the previous paper, we show twisted AR-quivers of type consist of the cluster point called twisted adapted cluster point. Hence, by introducing new combinatorial objects called twisted Dynkin quivers of type , 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