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An intrinsic analysis of unitarizable highest weight modules

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References

  1. Bourbaki, N.: Groupes et algèbres de Lie. Chaps. IV–VI, Act. Sci. Ind. 1337. Paris: Hermann 1968

    Google Scholar 

  2. Davidson, M.G., Enright, T.J., Stanke, R.J.: Differential operators and highest weight representations. preprint

  3. Dixmier, J.: Sur les représentations unitaires des groupes de Lie nilpotents IV. Can. J. Math.11, 321–344 (1959)

    Google Scholar 

  4. Dixmier, J.: Algebres enveloppantes cahiers scientifiques, No. 37. Paris: Gauthier-Villars 1974

    Google Scholar 

  5. Enright, T.J.: Analogues of Kostant's u cohomology formulas for unitary highest weight modules. j. Reine Angew. Math.392, 27–36 (1988)

    Google Scholar 

  6. Enright, T.J., Howe, R., Wallach, N.R.: A classification of unitary highest weight modules, in Representation theory of reductive groups. Trombi, P.C. (ed) 97–143. Boston: 1983

  7. Goncharov, A.B.: Constructions of the Weil representations of certain simple Lie algebras, Funct. Anal. Appl.16, 70–71 (1982)

    Google Scholar 

  8. Helgason, S.: Differential geometry and symmetric spaces. London: Academic Press 1962

    Google Scholar 

  9. Jakobsen, H.P.: Hermitian symmetric spaces and their unitary highest weight modules. J. Funct. Anal.52, 385–412 (1983)

    Google Scholar 

  10. Jantzen, J.C.: Moduln mit einem höchsten Gewicht. (Lect. Notes Math., Vol. 750). Berlin Heidelberg New York: Springer 1979

    Google Scholar 

  11. Johnson, K.D.: On the ring of invariant polynomials on a hermitian symmetric space. J. Algebra67, 72–81 (1980)

    Google Scholar 

  12. Joseph, A.: A preparation theorem for the prime spectrum of a semisimple Lie algebra. J. Algebra48, 241–289 (1977)

    Google Scholar 

  13. Kashiwara, M., Vergne, M.: On the Segal-Shale-Weil representations and harmonic polynomials. Invent. Math.44, 1–47 (1978)

    Article  Google Scholar 

  14. Kostant, B.: Verma modules and the existence of quasi-invariant differential operators, in Non-commutative harmonic analysis. Carmona, J., Dixmier, J., Vergne, M. (eds.) (Lect. Notes Math., Vol. 466) Berlin Heidelberg New York: Springer 1975

    Google Scholar 

  15. Kumar, S.: Proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture. Invent. Math.93, 117–130 (1988)

    Google Scholar 

  16. Levasseur, T., Stafford, J.T.: Rings of differential operators on classical rings of invariants. Mem. Amer. Math. Soc.412 (1989)

  17. Parthasarathy, K.P.: Criteria for the unitarizability of some highest weight modules. Proc. Indian Acad. Sci.89, 1–24 (1980)

    Google Scholar 

  18. Parthasarathy, K.R., Ranga Rao, R., Varadarajan, V.S.: Representations of complex Lie groups and Lie algebras. Ann. Math.85, 383–429 (1967)

    Google Scholar 

  19. Schmid, W.: Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen. Invent. Math.9, 61–80 (1969)

    Article  Google Scholar 

  20. Wallach, N.R.: The analytic continuation of the discrete series, I, II. T.A.M.S.251, 1–17, 19–37 (1979)

    Google Scholar 

  21. Wallach, N.R.: Real reductive group I. New York: Academic Press 1988

    Google Scholar 

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Author notes

  1. Anthony Joseph

    Present address: Laboratoire de Mathématiques Fondamentales, Equipe de recherche associée au CNRS, Université de Pierre et Marie Curie, 4 Place Jussieu, F-75232, Paris Cedex 05, France

Authors and Affiliations

  1. Department of Mathematics, University of California at San Diego, 92093, La Jolla, CA, USA

    Thomas J. Enright

  2. Department of Theoretical Mathematics, Weizmann Institute of Science, 76100, Rehovot, Israel

    Anthony Joseph

Authors
  1. Thomas J. Enright
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  2. Anthony Joseph
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This author has been supported in part by NSF Grant # DMS-8902425

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Enright, T.J., Joseph, A. An intrinsic analysis of unitarizable highest weight modules. Math. Ann. 288, 571–594 (1990). https://doi.org/10.1007/BF01444551

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