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)).
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