Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras
- 주제(키워드) Denominator formulas , Folded AR-quivers , Folded distance polynomials , Longest element , r-cluster point , Twisted AR-quivers , Twisted Coxeter elements
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- OA유형 Green Submitted
- 발행기관 Academic Press Inc.
- 발행년도 2019
- URI http://www.dcollection.net/handler/ewha/000000160786
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jalgebra.2019.06.013
초록/요약
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)). © 2019 Elsevier Inc.
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