Kazhdan-Lusztig polynomials of Dowling geometries

TL;DR

This paper provides a combinatorial interpretation of Kazhdan-Lusztig polynomial coefficients for Dowling geometries, extending understanding of these polynomials in matroid theory.

Contribution

It introduces a concrete combinatorial interpretation for Kazhdan-Lusztig polynomial coefficients of Dowling geometries and their equivariant versions.

Findings

Coefficients of Kazhdan-Lusztig polynomials are given a combinatorial interpretation.

Interpretation extends to equivariant Kazhdan-Lusztig and Z-polynomials.

Results apply to Dowling geometries associated with non-trivial groups.

Abstract

We give a concrete combinatorial interpretation of the coefficients of the Kazhdan-Lusztig polynomials of Dowling geometries, a family of matroids which generalizes braid matroids of types A and B. Furthermore, we interpret the coefficients of the equivariant Kazhdan-Lusztig polynomials and the equivariant Z-polynomials of Dowling geometries associated to non-trivial groups with respect to their full automorphism groups.