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

Proudfoot, Nicholas

Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 613-619.

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.

Classification : 05B35, 20C33
Mots clés : Kazhdan–Lusztig polynomial, matroid, unipotent representation

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