Twisted Coxeter elements and Folded AR-quivers via Dynkin diagram automorphisms:II
Abstract
As a continuation of the previous paper, we find a combinatorial interpretation of Dorey's rule for type Cn via twisted Auslander-Reiten quivers (AR-quivers) of type Dn+1, which are combinatorial AR-quivers related to certain Dynkin diagram automorphisms. Combinatorial properties of twisted AR-quivers are useful to understand not only Dorey's rule but also other notions in the representation theory of the quantum affine algebra Uq'(Cn(1)) such as denominator formulas. In addition, unlike twisted adapted classes of type A2n-1 in the previous paper, we show twisted AR-quivers of type Dn+1 consist of the cluster point called twisted adapted cluster point. Hence, by introducing new combinatorial objects called twisted Dynkin quivers of type Dn+1, we give one to one correspondences between twisted Coxeter elements, twisted adapted classes and twisted AR-quivers.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.