Automorphism groups of root systems matroids

Dutour Sikirić, M.; Felikson, A.; Tumarkin, P.

Abstract

Given a root system View the MathML source, the vector system View the MathML source is obtained by taking a representative v in each antipodal pair {v,−v}. The matroid View the MathML source is formed by all independent subsets of View the MathML source. 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 system matroids View the MathML source 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 system matroids.

Citation

Dutour Sikirić, M., Felikson, A., & Tumarkin, P. (2011). Automorphism groups of root systems matroids. European Journal of Combinatorics, 32(3), 383-389. https://doi.org/10.1016/j.ejc.2010.11.003

• Journal Article Type: Article
• Publication Date: 2011-04
• Deposit Date: Mar 19, 2012
• Journal: European Journal of Combinatorics
• Print ISSN: 0195-6698
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 32
• Issue: 3
• Pages: 383-389
• DOI: https://doi.org/10.1016/j.ejc.2010.11.003