10.1016/j.ejc.2021.103312

# Representations of automorphism groups on the homology of matroids

## Abstract

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 with the homology of the lattice of flats of \$M\$, and (when \$M\$ is realizable) with the top cohomology of a hyperplane arrangement. Finally we analyze in detail the case of the complete graph, which has applications to algebraic geometry

## Similar works

This paper was published in arXiv.org e-Print Archive.

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