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 $M^{\ast }$. 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.

中文翻译：

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类同拟素在拟阵上的表示

给定一组 $G$ 拟阵的同构关系 $\mathrm{中号}$，我们描述了 $G$ 对偶拟阵独立复合体的同源性 ${\mathrm{中号}}^{\ast }$。这些表示与平面的晶格的同源性有关。$\mathrm{中号}$， 什么时候 $\mathrm{中号}$是可实现的）到超平面布置的最高同调性。最后，我们详细分析完整图的情况，该图适用于代数几何。