Linear Simple Lie Algebras and Ranks of Operators

  • Yu. G. Zarhin
Part of the Progress in Mathematics book series (MBC, volume 88)


We discuss spectra of operators in irreducible finite-dimensional representations of simple Lie algebras. We give lower bounds for the rank of non-zero operators in the representations.


Weyl Group Simple Root Vector Subspace Coxeter Number Finite Linear Group 
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  1. [1]
    N. Bourbaki, Groups et algèbres de Lie, Chapitres 4, 5, 6, Hermann, Paris, 1968.Google Scholar
  2. [2]
    N. Bourbaki, Groupes et algèbres de Lie, Chapitres 7, 8, Hermann, Paris, 1975.MATHGoogle Scholar
  3. [3]
    V. Guillemin, D. Quillen, S. Sternberg, The classification of the irreducible complex algebras of infinite type, J. Analyse Math. 18 (1967), 107–112.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    B. Kostant, The characterization of classical groups, Duke Math. J. 25 (1958), 107–123.CrossRefMATHMathSciNetGoogle Scholar
  5. [5]
    T. A. Springer, Jordan algebras and algebraic groups. Springer-Verlag, Heidelberg, 1973.CrossRefMATHGoogle Scholar
  6. [6]
    Yu. G. Zarhin, Weights of simple Lie algebras in the cohomology of algebraic varieties, Math USSR Izvestija 24 (1985), 245–282.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Yu. G. Zarhin
    • 1
  1. 1.Research Computing Center USSRAcademy of SciencesMoscowUSSR

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