Lower bounds for Kazhdan-Lusztig polynomials from patterns

Details Lower bounds for Kazhdan-Lusztig polynomials from patterns Lower bounds for Kazhdan-Lusztig polynomials from patterns

2002-02-24

arxiv.org/abs/math/0202252v5

Mathematics

Representation Theory

14 pages; updated references. Final version; will appear in Transformation Groups vol.8, no. 4

Scientific paper

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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