Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras

Abstract

In this paper, we introduce twisted and folded AR-quivers of type A(2n+1), Dn+1, E-6 and D-4 associated to (triply) twisted Coxeter elements. Using the quivers of type A(2n+1) and Dn+1, we describe the denominator formulas and Dorey's rule for quantum affine algebras U-q'(B-n+1((1))) and U-q'(C-n((1))), which are important information of representation theory of quantum affine algebras. More precisely, we can read the denominator formulas for U-q'(B-n+1((1))) (resp. U-q'(C-n((1)))) using certain statistics on any folded AR-quiver of type A(2n+1) (resp. Dn+1) and Dorey's rule for U-q'(B-n+1((1))) (resp. U-q'(C-n((1)))) applying the notion of minimal pairs in a twisted AR-quiver. By adopting the same arguments, we propose the conjectural denominator formulas and Dorey's rule for U-q'(F-4((1))) and U-q'(G(2)((1))). (C) 2019 Elsevier Inc. All rights reserved.