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Subword complexes and edge subdivisions

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Abstract

For a finite Coxeter group, a subword complex is a simplicial complex associated with a pair (Q, π), where Q is a word in the alphabet of simple reflections and π is a group element. We discuss the transformations of such a complex that are induced by braid moves of the word Q. We show that under certain conditions, such a transformation is a composition of edge subdivisions and inverse edge subdivisions. In this case, we describe how the H- and γ-polynomials change under the transformation. This case includes all braid moves for groups with simply laced Coxeter diagrams.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Mikhail A. Gorsky

  2. UFR de Mathématiques, Case 7012, Institut de Mathématiques de Jussieu — Paris Rive Gauche, UMR 7586 du CNRS, Bât. Sophie Germain, Université Paris Diderot — Paris 7, 75205, Paris Cedex 13, France

    Mikhail A. Gorsky

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  1. Mikhail A. Gorsky
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Correspondence to Mikhail A. Gorsky.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Vol. 286, pp. 129–143.

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Gorsky, M.A. Subword complexes and edge subdivisions. Proc. Steklov Inst. Math. 286, 114–127 (2014). https://doi.org/10.1134/S0081543814060078

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  • DOI: https://doi.org/10.1134/S0081543814060078

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