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Lower bounds for Kazhdan-Lusztig polynomials from patterns

Sara Billey·Tom Braden
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Abstract

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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Sara Billey, Tom Braden. 2003-09-30. Lower bounds for Kazhdan-Lusztig polynomials from patterns. https://arxiv.org/abs/math/0202252

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