Publication details
Reflection groups and quiver mutation
Diagrammatics
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. Remarkably, such a diagram turns out to be 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 we show that each diagram encodes a natural presentation of the Weyl group as reflection group. The latter one extends work of Cameron, Seidel and Tsaranov as well as Barot and Marsh.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Article
- Journal
- Electronic Journal of Combinatorics
- Volume
- 32
- Pages
- 2-10
- No. of pages
- 9
- ISSN
- 1077-8926
- Publication date
- 25.04.2025
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Theoretical Computer Science, Geometry and Topology, Discrete Mathematics and Combinatorics, Computational Theory and Mathematics, Applied Mathematics
- Electronic version(s)
-
https://doi.org/10.37236/13369 (Access:
Open
)
https://arxiv.org/abs/1910.09421 (Access: Open )
