Abstract
In this paper, we discuss maximality of Seidel matrices with a fixed largest eigenvalue. We present a classification of maximal Seidel matrices of largest eigenvalue 3, which gives a classification of maximal equiangular lines in a Euclidean space with angle \(\arccos 1/3\). Motivated by the maximality of the exceptional root system \(E_8\), we define strong maximality of a Seidel matrix, and show that every Seidel matrix achieving the absolute bound is strongly maximal.
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Acknowledgements
We greatly thank Professor Min Xu for supporting M.-Y. Cao to visit University of Science and Technology of China. We also thank the referees for their comments. J.H. Koolen is partially supported by the National Natural Science Foundation of China (No. 12071454), Anhui Initiative in Quantum Information Technologies (No. AHY150000) and the project “Analysis and Geometry on Bundles” of Ministry of Science and Technology of the People’s Republic of China. A. Munemasa is partially supported by the JSPS KAKENHI grant (JP20K03537). K. Yoshino is supported by a scholarship from Tohoku University, Division for Interdisciplinary Advanced Research and Education.
Funding
J.H. Koolen is partially supported by the National Natural Science Foundation of China (No. 12071454), Anhui Initiative in Quantum Information Technologies (No. AHY150000) and the project “Analysis and Geometry on Bundles” of Ministry of Science and Technology of the People’s Republic of China. A. Munemasa is partially supported by the JSPS KAKENHI grant (JP20K03537). K. Yoshino is supported by a scholarship from Tohoku University, Division for Interdisciplinary Advanced Research and Education.
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Prof. Eiichi Bannai on the occasion of his 75th birthday.
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Cao, MY., Koolen, J.H., Munemasa, A. et al. Maximality of Seidel matrices and switching roots of graphs. Graphs and Combinatorics 37, 1491–1507 (2021). https://doi.org/10.1007/s00373-021-02359-w
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DOI: https://doi.org/10.1007/s00373-021-02359-w