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arXiv 2001.037602020-01math.RTmath.ATmath.CO

Representations of automorphism groups on the homology of matroids

Luca Moci, Gian Marco Pezzoli

发表信息：: European Journal of Combinatorics 94 (2021) 103312
DOI：: 10.1016/j.ejc.2021.103312

英文摘要：

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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