Publikationsdetails
Reflection groups and quiver mutation
Diagrammatics
- verfasst von
- Patrick Wegener
- 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.
- Organisationseinheit(en)
-
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
- Typ
- Artikel
- Journal
- Electronic Journal of Combinatorics
- Band
- 32
- Seiten
- 2-10
- Anzahl der Seiten
- 9
- ISSN
- 1077-8926
- Publikationsdatum
- 25.04.2025
- Publikationsstatus
- Veröffentlicht
- Peer-reviewed
- Ja
- ASJC Scopus Sachgebiete
- Theoretische Informatik, Geometrie und Topologie, Diskrete Mathematik und Kombinatorik, Theoretische Informatik und Mathematik, Angewandte Mathematik
- Elektronische Version(en)
-
https://doi.org/10.37236/13369 (Zugang:
Offen)
https://arxiv.org/abs/1910.09421 (Zugang: Offen)
