Document Type
Article
Date
8-7-2006
Disciplines
Mathematics
Description/Abstract
This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence classes of the above sequences is a partially ordered set that contains a great deal of information about the preprojective component of the Auslander-Reiten quiver. The results apply to the study of reduced words in the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix.
Recommended Citation
Kleiner, Mark and Tyler, Helene R., "Sequences of Reflection Functors and the Preprojective Component of a Valued Quiver" (2006). Mathematics - All Scholarship. 77.
https://surface.syr.edu/mat/77
Source
Harvested from arXiv.org
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Additional Information
This manuscript is from arXiv.org, for more information see http://arxiv.org/abs/math/0608175