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Lower bounds for Kazhdan-Lusztig polynomials from patterns

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arxiv math/0202252 v5 pith:Z5S43ROZ submitted 2002-02-24 math.RT math.AGmath.CO

Sara Billey , Tom Braden This is my paper · ORCID
classification math.RTmath.AGmath.CO
keywords patternslowermathpatternweylavoidanceboundbounds
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We give a lower bound for the value at q=1 of a Kazhdan-Lustig polynomial in a Weyl group W in terms of "patterns''. This is expressed by a "pattern map" from W to W' for any parabloic subgroup W'. This notion generalizes the concept of patterns and pattern avoidance for permutations to all Weyl groups. The main tool of the proof is a "hyperbolic localization" on intersection cohomology; see the related paper http://front.math.ucdavis.edu/math.AG/0202251

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  1. Big data approach to Kazhdan-Lusztig polynomials

    math.RT 2024-12 conditional novelty 6.0 of 10

    Data on Kazhdan-Lusztig polynomials up to S_11 suggests superexponential growth of extremal coefficients, near-universal unimodality, and a conjectured closed family (1+v+...+v^l)^{k-1}.

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