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

Uhi Rinn Suh, Se jin Oh

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper, we introduce twisted and folded AR-quivers of type A2n+1, Dn+1, E6 and D4 associated to (triply) twisted Coxeter elements. Using the quivers of type A2n+1 and Dn+1, we describe the denominator formulas and Dorey's rule for quantum affine algebras Uq (Bn+1 (1)) and Uq (C(1) n), which are important information of representation theory of quantum affine algebras. More precisely, we can read the denominator formulas for Uq (Bn+1 (1)) (resp. Uq (Cn (1))) using certain statistics on any folded AR-quiver of type A2n+1 (resp. Dn+1) and Dorey's rule for Uq (Bn+1 (1)) (resp. Uq (Cn (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 Uq (F4 (1)) and Uq (G2 (1)).

Original languageEnglish
Pages (from-to)53-132
Number of pages80
JournalJournal of Algebra
Volume535
DOIs
StatePublished - 1 Oct 2019

Keywords

  • Denominator formulas
  • Folded AR-quivers
  • Folded distance polynomials
  • Longest element
  • Twisted AR-quivers
  • Twisted Coxeter elements
  • r-cluster point

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