5 research outputs found

    A simple characterization of special matchings in lower Bruhat intervals

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    We give a simple characterization of special matchings in lower Bruhat intervals (that is, intervals starting from the identity element) of a Coxeter group. As a byproduct, we obtain some results on the action of special matchings.Comment: accepted for publication on Discrete Mathematic

    A simple characterization of special matchings in lower Bruhat intervals

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    We give a simple characterization of special matchings in lower Bruhat intervals (that is, intervals starting from the identity element) of a Coxeter group. As a byproduct, we obtain some results on the action of special matchings.Comment: accepted for publication on Discrete Mathematic

    The combinatorial invariance conjecture for parabolic Kazhdan-Lusztig polynomials of lower intervals

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    The aim of this work is to prove a conjecture related to the Combinatorial Invariance Conjecture of Kazhdan-Lusztig polynomials, in the parabolic setting, for lower intervals in every arbitrary Coxeter group. This result improves and generalizes, among other results, the main results of [Advances in Math. {202} (2006), 555-601], [Trans. Amer. Math. Soc. {368} (2016), no. 7, 5247--5269].Comment: to appear in Advances in Mathematic

    Pircon kernels and up-down symmetry

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    We show that a symmetry property that we call the up-down symmetry implies that the Kazhdan--Lusztig RxR^x-polynomials of a pircon PP are a PP-kernel, and we show that this property holds in the classical cases. Then, we enhance and extend to this context a duality of Deodhar in parabolic Kazhdan--Lusztig theory.Comment: to appear in Journal of Algebra. arXiv admin note: substantial text overlap with arXiv:1907.0085
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