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| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 21 Oct 2019 |
| Externally published | Yes |
Abstract
Keywords
- math.CO, math.GR
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2019.
Research output: Working paper/Preprint › Preprint
}
TY - UNPB
T1 - Reflection groups and quiver mutation: Diagrammatics
AU - Wegener, Patrick
PY - 2019/10/21
Y1 - 2019/10/21
N2 - 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.
AB - 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.
KW - math.CO
KW - math.GR
M3 - Preprint
BT - Reflection groups and quiver mutation: Diagrammatics
ER -