Year: 2025
Type: article
Abstract: We extend Carter's notion of admissible diagrams and attach a Dynkin-like diagram to each reduced reflection factorization of an element in a finite Weyl group. We give a complete classification for the diagrams attached to reduced reflection factorizations. We show that such a diagram is cyclically orientable if and only if it is isomorphic to the underlying graph of a quiver which is mutation-equivalent to a Dynkin quiver. Furthermore, these diagrams encode a natural presentation of the Weyl group as reflection group, as shown by Cameron-Seidel-Tsaranov (1994) as well as Barot-Marsh (2015).
DOI: 10.37236/13369
Author: Patrick Wegener
Institution: Leibniz University Hannover
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409766485