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Structure of representations generated by vectors of highest weight

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Literature Cited

  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).

  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. 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. Lie Topological Groups. Theory of Lie Algebras [Russian translation], IL, Moscow (1962).

    Google Scholar 

  5. J.-P. Serre, Lie Algebras and Lie Groups [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  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. B. Kostant, "A formula for the multiplicity of a weight," Trans. Amer. Math. Soc.,93, 53–73 (1959).

    Google Scholar 

  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. N. Bourbaki, Groupes et Algebres de Lie, Hermann (1968), Chaps. 4–6.

  10. B. Kostant, "Lie algebra cohomology and generalized Schubert cells," Ann. Math.,77, 72–144 (1963).

    Google Scholar 

  11. D.-N. Verma, "Structure of certain induced representations of complex semisimple Lie algebras," Dissertation, Yale Univ. (1966).

  12. O. Zariski and P. Samuel, Commutative Algebra, Vol. 1, Van Nostrand (1958).

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Authors
  1. I. N. Bernshtein
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  2. I. M. Gel'fand
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  3. S. I. Gel'fand
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Additional information

Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 5, No. 1, pp. 1–9, January–March, 1971.

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Bernshtein, I.N., Gel'fand, I.M. & Gel'fand, S.I. Structure of representations generated by vectors of highest weight. Funct Anal Its Appl 5, 1–8 (1971). https://doi.org/10.1007/BF01075841

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  • DOI: https://doi.org/10.1007/BF01075841

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