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On generation of the root lattice by roots


Let Φ be a root system and let Γ ⊆ Φ. In this short paper we prove that Γ contains a -basis of the lattice that it generates.

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[1] A. Borel and J. de Siebenthal . Les sous-groupes fermé de rank maximum des groupes de Lie clos. Comment. Math. Helv. 23 (1949), 200221.

[3] E. B. Dynkin . Semisimple subalgebras of semisimple Lie algebras. Trans. Amer. Math. Soc. (2) 6 (1957), 111244.

[4] S. M. Goodwin . On the conjugacy classes in maximal unipotent subgroups of simple algebraic groups. Transform. Groups 11, no. 1 (2006), 5176.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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