Equivariant Kazhdan-Lusztig polynomials of $q$-niform matroids
Combinatorics
2018-09-05 v2 Group Theory
Abstract
We introduce -analogues of uniform matroids, which we call -niform matroids. While uniform matroids admit actions of symmetric groups, -niform matroids admit actions of finite general linear groups. We show that the equivariant Kazhdan-Lusztig polynomial of a -niform matroid is the unipotent -analogue of the equivariant Kazhdan-Lusztig polynomial of the corresponding uniform matroid, thus providing evidence for the positivity conjecture for equivariant Kazhdan-Lusztig polynomials.
Keywords
Cite
@article{arxiv.1808.07855,
title = {Equivariant Kazhdan-Lusztig polynomials of $q$-niform matroids},
author = {Nicholas Proudfoot},
journal= {arXiv preprint arXiv:1808.07855},
year = {2018}
}
Comments
References added; typos corrected