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

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

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