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

Title
Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras
Authors
Suh U.R.Oh S.-J.
Ewha Authors
오세진
SCOPUS Author ID
오세진scopus
Issue Date
2019
Journal Title
Journal of Algebra
ISSN
0021-8693JCR Link
Citation
Journal of Algebra vol. 535, pp. 53 - 132
Keywords
Denominator formulasFolded AR-quiversFolded distance polynomialsLongest elementr-cluster pointTwisted AR-quiversTwisted Coxeter elements
Publisher
Academic Press Inc.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
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)). © 2019 Elsevier Inc.
DOI
10.1016/j.jalgebra.2019.06.013
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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