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arXiv · 0810.0842

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

Brent G. Pohlmann
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Abstract

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.

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BibTeXRIS

Brent G. Pohlmann. 2008-10-05. Structural properties of acyclic heaps of pieces with Kazhdan--Lusztig theory. https://arxiv.org/abs/0810.0842

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