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Sequences of reflection functors and the preprojective component of a valued quiver

Mark Kleiner·Helene R. Tyler
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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.

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BibTeXRIS

Mark Kleiner, Helene R. Tyler. 2006-08-07. Sequences of reflection functors and the preprojective component of a valued quiver. https://arxiv.org/abs/math/0608175

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