# ALGEBRAIC COMBINATORICS

Equivariant Kazhdan–Lusztig polynomials of $q$-niform matroids
Algebraic Combinatorics, Volume 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.

Accepted:
Revised after acceptance:
Published online:
DOI: 10.5802/alco.59
Classification: 05B35,  20C33
Keywords: Kazhdan–Lusztig polynomial, matroid, unipotent representation
Proudfoot, Nicholas 1

1 University of Oregon Department of Mathematics Eugene OR 97403, USA
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Proudfoot, Nicholas. Equivariant Kazhdan–Lusztig polynomials of $q$-niform matroids. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 613-619. doi : 10.5802/alco.59. https://alco.centre-mersenne.org/articles/10.5802/alco.59/

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