manuscripta mathematica

, Volume 88, Issue 1, pp 59–72 | Cite as

On the structure of an α-stratified generalized Verma module over Lie algebrasl(n, ℂ))

  • Vladimir Mazorchuk


We study α-stratified modules of Verma type for the Lie algebrasl(n, ℂ). Necessary and sufficient conditions are established for existence of a submodule in a generalized Verma module.


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  1. 1.
    I. N. Bernstein, I. M. Gelfand andS. I. Gelfand, The structure of representation generated by vector of highest weight., Functional Anal. Appl. 5, 1–9 (1971)CrossRefMathSciNetGoogle Scholar
  2. 2.
    A. J. Coleman, V. M. Futorny, StratifiedL-modules, Mathematical Preprint #1990-15Google Scholar
  3. 3.
    J. Dixmier, Algebras enveloppants, Ganthier Villars, Paris, 1974Google Scholar
  4. 4.
    Yu. A. Drozd, S. A. Ovsienko andV. M. Futorny, S-homomorphism of Harish-Chandra and\(\mathfrak{G}\) generated by semiprimitive elements// Ukrainian Math. J. 42, 1032–1037 (1990)MathSciNetGoogle Scholar
  5. 5.
    S. L. Fernando, Simple weight modules of complex reductive Lie algebras., Ph. D. Thesis, Univ. of Wisconsin, 1983.Google Scholar
  6. 6.
    V. M. Futorny, A generalization of Verma modules and irreducible representations of the Lie algebrasl(3, ℂ)// Ukrainian Math. J. 38, 422–427 (1986)CrossRefMathSciNetGoogle Scholar
  7. 7.
    V. M. Futorny, Weightsl(3)-modules, generated by semiprimitive element.// Ukrainian Math. J. 43, 281–285 (1991)CrossRefMathSciNetGoogle Scholar
  8. 8.
    V. M. Futorny, The weight representation of semisimple finitedimentional Lie algebras., Ph. D. Thesis, Univ. of Kiev, 1987Google Scholar
  9. 9.
    J. Lepowsky, Generalized Verma modules, the Cartan-Helgason theorem and the Harish-Chandra isomorphism., J. Algebra 49, 470–495 (1977)CrossRefMathSciNetGoogle Scholar
  10. 10.
    V. S. Mazorchuk, α-stratified modules over Lie algebrasl(n, ℂ)// Ukrainian Math. J. 45, 1215–1224 (1993)CrossRefMathSciNetGoogle Scholar
  11. 11.
    D. N. Verma, Structure of representation of complex semisimple Lie algebras.// Bull. Amer. Math. Soc. 74, 160–166 (1986)Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Vladimir Mazorchuk
    • 1
  1. 1.Faculty of Mechanics and MethematicsKiev UniversityKievUkraine

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