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

Nicholas Proudfoot
2019 Algebraic Combinatorics  
We study 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. Theorem 1.1.
more » ... Let C i n,m be the coefficient of t i in the S n -equivariant Kazhdan-Lusztig polynomial of U n,m , and let c i n,m := dim C i n,m be the corresponding non-equivariant coefficient.
doi:10.5802/alco.59 fatcat:magyfv5xnjgh3okc7sohhc7o2u