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

Mark Kleiner, Helene R. Tyler

Research output: Contribution to journalArticlepeer-review

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 with an indecomposable symmetrizable generalized Cartan matrix.

Original languageEnglish (US)
Pages (from-to)718-726
Number of pages9
JournalJournal of Pure and Applied Algebra
Volume212
Issue number4
DOIs
StatePublished - Apr 2008

ASJC Scopus subject areas

  • Algebra and Number Theory

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