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 language | English |
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Pages (from-to) | 53-132 |
Number of pages | 80 |
Journal | Journal of Algebra |
Volume | 535 |
DOIs | |
State | Published - 1 Oct 2019 |
Bibliographical note
Funding Information:This work was supported by the New Faculty Startup Fund from Seoul National University, NRF Grant # 2016R1C1B1010721 and # 2019R1F1A1059363.This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2019R1A2C4069647).
Publisher Copyright:
© 2019 Elsevier Inc.
Keywords
- Denominator formulas
- Folded AR-quivers
- Folded distance polynomials
- Longest element
- Twisted AR-quivers
- Twisted Coxeter elements
- r-cluster point