Representations of automorphism groups on the homology of matroids

Given a group G of automorphisms of a matroid M, we describe the representations of G on the homology of the independence complex of the dual matroid M∗ . These representations are related to the homology of the lattice of flats of M, and (when M is realizable) to the top cohomology of a hyperplane arrangement. Finally, we analyze in detail the case of the complete graph, which has applications to algebraic geometry.