The equivariant Kazhdan-Lusztig polynomial of a matroid

Abstract

We define the equivariant Kazhdan-Lusztig polynomial of a matroid equipped with a group of symmetries, generalizing the nonequivariant case. We compute this invariant for arbitrary uniform matroids and for braid matroids of small rank.

arXiv comment26 pages

References in corpus (4)

• Representation theory and homological stability
• Mixed Hodge structures of configuration spaces
• Representation stability for cohomology of configuration spaces in ${\mathbf{R}}^d$
• The Kazhdan-Lusztig polynomial of a matroid

Cited by in corpus (4)

• Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures
• Kazhdan-Lusztig polynomials of braid matroids
• Partial flag incidence algebras
• Equivariant log-concavity of graph matchings