The algebraic geometry of Kazhdan-Lusztig-Stanley polynomials
Algebraic Geometry
2018-06-15 v2 Combinatorics
Abstract
Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups, rational polytopes, and realizable matroids, one can count points over finite fields on flag varieties, toric varieties, or reciprocal planes to obtain cohomological interpretations of these polynomials. We survey these results and unite them under a single geometric framework.
Keywords
Cite
@article{arxiv.1712.01250,
title = {The algebraic geometry of Kazhdan-Lusztig-Stanley polynomials},
author = {Nicholas Proudfoot},
journal= {arXiv preprint arXiv:1712.01250},
year = {2018}
}