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

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 $U_q^{\prime }(B_{n+1}^{(1)})$ such as Dorey's rule and denominator formulas.

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

References in corpus (1)

• 2-Kac-Moody algebras

Cited by in corpus (3)

• Quantum Grothendieck ring isomorphisms, cluster algebras and Kazhdan-Lusztig algorithm
• Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras
• Categorical relations between Langlands dual quantum affine algebras: Doubly laced types