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

Se-jin Oh; Uhi Rinn Suh

doi:10.1016/j.jalgebra.2019.06.013

paper

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

arXiv:2011.03611 · doi:10.1016/j.jalgebra.2019.06.013

Abstract

In this paper, we introduce twisted and folded AR-quivers of type $A_{2 n + 1}$ , $D_{n + 1}$ , $E_{6}$ and $D_{4}$ associated to (triply) twisted Coxeter elements. Using the quivers of type $A_{2 n + 1}$ and $D_{n + 1}$ , 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 $A_{2 n + 1}$ (resp. $D_{n + 1}$ ) 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 $U_{q}^{'} (G_{2}^{(1)})$ .

This is a megred version of arXiv:1606.00076 and arXiv:1606.00102. This version is published in Journal of Algebra. We upload this for reder's convenience

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

Abstract

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