arXiv Analytics

Sign in

arXiv:math/0202252 [math.RT]AbstractReferencesReviewsResources

Lower bounds for Kazhdan-Lusztig polynomials from patterns

Sara Billey, Tom Braden

Published 2002-02-24, updated 2003-09-30Version 5

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

Comments: 14 pages; updated references. Final version; will appear in Transformation Groups vol.8, no. 4
Categories: math.RT, math.AG, math.CO
Subjects: 14M15, 20F55
Related articles: Most relevant | Search more
arXiv:1003.3633 [math.RT] (Published 2010-03-18, updated 2010-10-26)
Quiver Varieties with Multiplicities, Weyl Groups of Non-Symmetric Kac-Moody Algebras, and Painlevé Equations
arXiv:1402.3431 [math.RT] (Published 2014-02-14)
A positivity conjecture for the Alvis-Curtis dual of the intersection cohomology of a Deligne-Lusztig variety
arXiv:2303.09251 [math.RT] (Published 2023-03-16)
Parabolic recursions for Kazhdan-Lusztig polynomials and the hypercube decomposition

Links

Toolbox