Equivariant Kazhdan-Lusztig polynomials of q-niform matroids [article]

Nicholas Proudfoot
2018 arXiv   pre-print
We introduce q-analogues of uniform matroids, which we call q-niform matroids. While uniform matroids admit actions of symmetric groups, q-niform matroids admit actions of finite general linear groups. We show that the equivariant Kazhdan-Lusztig polynomial of a q-niform matroid is the unipotent q-analogue of the equivariant Kazhdan-Lusztig polynomial of the corresponding uniform matroid, thus providing evidence for the positivity conjecture for equivariant Kazhdan-Lusztig polynomials.
arXiv:1808.07855v2 fatcat:brt6flnrpradbbnel2imxutdou