an:07089140
Zbl 1417.05024
Proudfoot, Nicholas
Equivariant Kazhdan-Lusztig polynomials of \(q\)-niform matroids
EN
Algebr. Comb. 2, No. 4, 613-619 (2019).
00436303
2019
j
05B35 05C31 52B40 20C33
Kazhdan-Lusztig polynomial; matroid; unipotent representation
Summary: 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.