TY - JOUR

T1 - Sequences of reflection functors and the preprojective component of a valued quiver

AU - Kleiner, Mark

AU - Tyler, Helene R.

N1 - Funding Information:
The first-named author is supported by the NSA grant H98230-06-1-0043. The paper was written when the second-named author visited Syracuse University in June of 2004 and in July of 2006 with a partial support of a Summer Research Grant from Manhattan College. She expresses her sincere gratitude to the college for their generosity and to the members of the Syracuse University Mathematics Department for their warm hospitality.

PY - 2008/4

Y1 - 2008/4

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jpaa.2007.06.014

DO - 10.1016/j.jpaa.2007.06.014

M3 - Article

AN - SCOPUS:36148999873

VL - 212

SP - 718

EP - 726

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

IS - 4

ER -