English

Equivariant Kazhdan-Lusztig polynomials of $q$-niform matroids

Combinatorics 2018-09-05 v2 Group Theory

Abstract

We introduce qq-analogues of uniform matroids, which we call qq-niform matroids. While uniform matroids admit actions of symmetric groups, qq-niform matroids admit actions of finite general linear groups. We show that the equivariant Kazhdan-Lusztig polynomial of a qq-niform matroid is the unipotent qq-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