Kazhdan-Lusztig polynomials of Dowling geometries

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.