Functional Analysis and Its Applications

, Volume 5, Issue 1, pp 1–8 | Cite as

Structure of representations generated by vectors of highest weight

  • I. N. Bernshtein
  • I. M. Gel'fand
  • S. I. Gel'fand
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    I. M. Gel'fand, "Cohomologies of infinite-dimensional Lie algebras; some questions of integral geometry" [in Russian], Report to the International Mathematical Congress (1970).Google Scholar
  2. 2.
    D.-N. Verma, "Structure of certain induced representations of complex semisimple Lie algebras," Bull. Amer. Math. Soc.,74, 160–166 (1968).Google Scholar
  3. 3.
    Harish-Chandra, "On some applications of universal enveloping algebra of a semisimple Lie algebra," Trans. Amer. Math. Soc.,70, 28–96 (1951).Google Scholar
  4. 4.
    Lie Topological Groups. Theory of Lie Algebras [Russian translation], IL, Moscow (1962).Google Scholar
  5. 5.
    J.-P. Serre, Lie Algebras and Lie Groups [Russian translation], Mir, Moscow (1969).Google Scholar
  6. 6.
    I. M. Gel'fand and M. I. Graev, "Fourier transforms of rapidly decreasing functions on complex semisimple groups," Dokl. Akad. Nauk SSSR,131, No. 3, 496–499 (1960).Google Scholar
  7. 7.
    B. Kostant, "A formula for the multiplicity of a weight," Trans. Amer. Math. Soc.,93, 53–73 (1959).Google Scholar
  8. 8.
    K. R. Parthasarathy, Rao R. Ranga, and V. S. Varadarajan, "Representations of complex semisimple Lie groups and Lie algebras," Ann. Math.,85, 383–429 (1967).Google Scholar
  9. 9.
    N. Bourbaki, Groupes et Algebres de Lie, Hermann (1968), Chaps. 4–6.Google Scholar
  10. 10.
    B. Kostant, "Lie algebra cohomology and generalized Schubert cells," Ann. Math.,77, 72–144 (1963).Google Scholar
  11. 11.
    D.-N. Verma, "Structure of certain induced representations of complex semisimple Lie algebras," Dissertation, Yale Univ. (1966).Google Scholar
  12. 12.
    O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Van Nostrand (1958).Google Scholar

Copyright information

© Consultants Bureau 1971

Authors and Affiliations

  • I. N. Bernshtein
  • I. M. Gel'fand
  • S. I. Gel'fand

There are no affiliations available

Personalised recommendations