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arXiv · 0711.4670

Automorphism groups of root systems matroids

Mathieu Dutour Sikiric·Anna Felikson·Pavel Tumarkin
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Abstract

Given a root system $\mathsf{R}$, the vector system $\tilde{\mathsf{R}}$ is obtained by taking a representative $v$ in each antipodal pair $\{v, -v\}$. The matroid $M(\mathsf{R})$ is formed by all independent subsets of $\tilde{\mathsf{R}}$. The automorphism group of a matroid is the group of permutations preserving its independent subsets. We prove that the automorphism groups of all irreducible root systems matroids $M(\mathsf{R})$ are uniquely determined by their independent sets of size 3. As a corollary, we compute these groups explicitly, and thus complete the classification of the automorphism groups of root systems matroids.

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Mathieu Dutour Sikiric, Anna Felikson, Pavel Tumarkin. 2008-11-25. Automorphism groups of root systems matroids. https://arxiv.org/abs/0711.4670

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