Automorphism groups of root systems matroids

Details Automorphism groups of root systems matroids Automorphism groups of root systems matroids

2007-11-29

arxiv.org/abs/0711.4670v3

Mathematics

Combinatorics

9 pages, 1 table

Scientific paper

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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