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

Se-jin Oh; UhiRinn Suh

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

Representation Theory 2016-10-28 v2 Combinatorics Quantum Algebra

Authors: Se-jin Oh , UhiRinn Suh

Abstract

We introduce and study the twisted adapted $r$ -cluster point and its combinatorial Auslander-Reiten quivers, called twisted AR-quivers and folded AR-quivers, of type $A_{2n+1}$ which are closely related to twisted Coxeter elements and the non-trivial Dynkin diagram automorphism. As applications of the study, we prove that folded AR-quivers encode crucial information on the representation theory of quantum affine algebra $U_q'(B^{(1)}_{n+1})$ such as Dorey's rule and denominator formulas.

Keywords

twisted k-theory cluster algebras coxeter groups

Cite

@article{arxiv.1606.00076,
  title  = {Twisted Coxeter elements and folded AR-quivers via Dynkin diagram automorphisms: I},
  author = {Se-jin Oh and UhiRinn Suh},
  journal= {arXiv preprint arXiv:1606.00076},
  year   = {2016}
}

Comments

We rewrite our introduction. Our approach using the Dynkin diagram folding can be distinguished from well-known techniques on non-simply laced types via Dynkin diagram folding of simply laced types

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

Abstract

Keywords

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