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Surjective Linear Maps Between Root Systems with Zero

  • D. Ž. Đoković (a1) and Nguyêñ Q. Thãńg
Abstract

If R 1 and R 2 are root systems and there is a linear map which maps R 1 ∪{0} onto R 2∪{0} we write R 1 —> R 2. We determine all pairs (R 1, R 2) of irreducible root systems such that R 1 —> R 2.

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References
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[B] Borel, A., Linear algebraic groups, Graduate Texts in Math., Second edition, New York, 1991.
[Bo] Bourbaki, N., Groupes et algèbres de Lie, Chapitres IV—VI, Hermann, Paris, 1968.
[BS] Burris, S. and Sankappanavar, H. P., A course in universal algebra, Springer, New York, 1981.
[OV] Onishchik, A. L. and Vinberg, E. B., Lie groups and algebraic groups, Springer, New York, 1990.
[Se] Selbach, M., Klassifikationstheorie der halbeinfacher algebraischer Gruppen, Bonner Math. Schriften 83(1976).
[St] Steinberg, R., Lectures on Chevalley groups, Yale University, 1967.
[Ti] Tits, J., Classification of algebraic semisimple groups, Proc. Sympos. Pure Math. IX(1966), 3262.
[Wa] Warner, G., Harmonic analysis on semisimple Lie groups, 1, Springer, New York, 1972.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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