Structural properties of acyclic heaps of pieces with Kazhdan--Lusztig theory

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We introduce the notions of boundary vertex, linear equivalence and effective boundary vertex in the context of Viennot's heaps of pieces. We prove that in the heap of a fully commutative element in a star reducible Coxeter group, every boundary vertex is linearly equivalent to an effective boundary vertex. Using this result, we establish Property W (in the sense of math.QA/0509363) for star reducible Coxeter groups; this corrects a mistake in the latter paper.
Ph.D. thesis, University of Colorado, 2008. Advisor: R.M. Green. 21 figures

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Combinatorics, Quantum Algebra, 20F55, 20C08

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http://salesiana.dossiersoluciones.com/handle/123456789/170752

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0810.0842
 http://arxiv.org/abs/0810.0842

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arXiv