Equivariant Kazhdan-Lusztig polynomials of q-niform matroids

2018/08/23 by Nicholas Proudfoot, Proudfoot, Nicholas · 1 citation
Mathematics · #05B35 #20C33 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1808.07855

openalex publication_date 2018/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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