Preprojective representations of valued quivers and reduced words in the Weyl group of a Kac-Moody algebra

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dc.creatorKleiner, Mark
dc.creatorPelley, Allen
dc.date2006-08-24
dc.date.accessioned2026-07-07T07:22:08Z
dc.date.available2026-07-07T07:22:08Z
dc.descriptionThis paper studies connections between the preprojective representations of a valued quiver, the (+)-admissible sequences of vertices, and the Weyl group by associating to each preprojective representation a canonical (+)-admissible sequence. A (+)-admissible sequence is the canonical sequence of some preprojective representation if and only if the product of simple reflections associated to the vertices of the sequence is a reduced word in the Weyl group. As a consequence, for any Coxeter element of the Weyl group associated to an indecomposable symmetrizable generalized Cartan matrix, the group is infinite if and only if the powers of the element are reduced words. The latter strengthens known results of Howlett, Fomin-Zelevinsky, and the authors.
dc.identifierhttps://arxiv.org/abs/math/0608612
dc.identifierhttp://arxiv.org/abs/math/0608612
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115550
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject16G20; 16G70; 20F55
dc.titlePreprojective representations of valued quivers and reduced words in the Weyl group of a Kac-Moody algebra
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