Reflection groups and quiver mutation: diagrammatics
The electronic journal of combinatorics, Tome 32 (2025) no. 2
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
Classification :
20F55, 05E10, 05E18
Mots-clés : reflection group, Carter diagram, quiver mutation, Dynkin quiver, Weyl group, finite Coxeter group
Mots-clés : reflection group, Carter diagram, quiver mutation, Dynkin quiver, Weyl group, finite Coxeter group
Affiliations des auteurs :
Patrick Wegener 1
@article{10_37236_13369,
author = {Patrick Wegener},
title = {Reflection groups and quiver mutation: diagrammatics},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13369},
zbl = {1567.20101},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13369/}
}
Patrick Wegener. Reflection groups and quiver mutation: diagrammatics. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13369
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