Lower bounds for Kazhdan-Lusztig polynomials from patterns
Representation Theory
2007-05-23 v5 Algebraic Geometry
Combinatorics
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
Cite
@article{arxiv.math/0202252,
title = {Lower bounds for Kazhdan-Lusztig polynomials from patterns},
author = {Sara Billey and Tom Braden},
journal= {arXiv preprint arXiv:math/0202252},
year = {2007}
}
Comments
14 pages; updated references. Final version; will appear in Transformation Groups vol.8, no. 4