Skip to main content
SpringerLink
Log in

Unitary derived functor modules with small spectrum

  • Published:
Acta Mathematica

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Adams, J., Some results on the dual pair (O(p, q), Sp(2m)). Yale University thesis, May 1981.

  2. Boe, B., Homomorphisms between generalized Verma modules. Preprint.

  3. Bourbaki, N.,Groupes et Algébres de Lie. Chapter VI, Hermann, 1968.

  4. Enright, T. J., On the fundamental series of a real semisimple Lie algebra: their irreducibility, resolutions and multiplicity formulae.Ann. of Math., 110 (1979), 1–82.

    Article  MATH  MathSciNet  Google Scholar 

  5. Enright, T. J., Unitary representations for two real forms of a semisimple Lie algebra: a theory of comparison.Lecture Notes in Mathematics, 1024. Springer-Verlag, 1983

  6. Enright, T. J. &Wallach, N. R., Notes on homological algebra and representations of Lie algebras.Duke Math. J., 47 (1980), 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  7. Enright, T. J., Howe, R. &Wallach, N. R., A classification of unitary highest weight modules.Representation Theory of Reductivy Groups (editor P. Trombi). Birkhäuser, Boston, 1982.

    Google Scholar 

  8. Enright, T. J., Parthasarathy, R., Wallach, N. R. &Wolf, J. A., Classes of unitarizable derived functor modules.Proc. Nat. Acad. Sci. U.S.A., 80 (1983), 7047–7050.

    MATH  Google Scholar 

  9. Enright, T. J. & Wolf, J. A., Continuation of unitary derived functor modules out of the canonical chamber. To appear inMemoires Math. Soc. France, 1984.

  10. Flensted-Jensen, M., Discrete series for semisimple symmetric spaces.Ann. of Math., 111 (1980), 253–311.

    Article  MATH  MathSciNet  Google Scholar 

  11. Garland, H. &Zuckerman, G., On unitarizable highest weight modules of Hermitian parirs.J. Fac. Sci. Univ. Tokyo, 28 (1982), 877–889.

    MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Jantzen, J. C., Kontravariante Formen auf induzierten Darstellungen halbeinfacher Lie-Algebren.Math. Ann., 226 (1977), 53–65.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. Matsuki, T. & Oshima, T., A description of discrete series for semisimple symmetric spaces. To appear inAdvanced Studies in Pure Mathematics.

  16. Parthasarathy, R., An algebraic construction of a class of representations of a semisimple Lie algebra.Math. Ann., 226 (1977), 1–52.

    Article  MATH  MathSciNet  Google Scholar 

  17. —, A generalization of the Enright-Varadarajan modules.Compositio Math., 36 (1978), 53–73.

    MATH  MathSciNet  Google Scholar 

  18. —, Criteria for unitarizability of some highest weight modules.Proc. Indian Acad. Sci., 89 (1980), 1–24.

    Article  MATH  MathSciNet  Google Scholar 

  19. Rawnsley, J., Schmid, W. & Wolf, J., Singular unitary representations and indefinite harmonic theory. To appear inJ. Funct. Anal., 1983.

  20. Schlichtkrull, H., A series of unitary irreducible representations induced from a symmetric subgroup of a semisimple Lie group.Invent. Math., 68 (1982), 497–516.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  22. —, Some properties of square integrable representations of semisimple Lie groups.Ann. of Math., 102 (1975), 535–564.

    Article  MATH  MathSciNet  Google Scholar 

  23. Shapovalov, N. N., On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra.Functional Anal. Appl., 6 (1972), 307–312.

    Article  MATH  Google Scholar 

  24. Speh, B., Unitary representations ofGL(n,R) with non-trivial (g, K)-cohomology.Invent. Math., 71 (1983), 443–465.

    Article  MATH  MathSciNet  Google Scholar 

  25. Vogan, Jr, D.,Representations of real reductive Lie groups. Birkhäuser, Boston-Basel-Stuttgart, 1981.

    MATH  Google Scholar 

  26. —, Singular unitary representations,Non Commutative Harmonic Analysis and Lie Groups. Lecture Notes in Mathematics, 880. Springer-Verlag, Berlin-Heidelberg-New York, 1981.

    Google Scholar 

  27. Vogan, Jr, D., Unitarizability of certain series of representations. Preprint.

  28. Vogan, Jr, D. & Zuckerman, G., Unitary representations with non-zero cohomology. Preprint.

  29. Wallach, N., The analytic continuation of the discrete series I, II.Trans. Amer. Math. Soc., 251 (1979), 1–17, 19–37.

    Article  MATH  MathSciNet  Google Scholar 

  30. Weyl, H.,The Classical Groups. Princeton University Press, 1946.

Download references

Author information

Authors and Affiliations

  1. University of California, San Diego, La Jolla, CA, USA

    T. J. Enright

  2. Tata Institute of Fundamental Research, Bombay, India

    R. Parthasarathy

  3. Rutgers University, New Brunswick, N.J., USA

    N. R. Wallach

  4. University of California, Berkeley, CA, USA

    J. A. Wolf

Authors
  1. T. J. Enright
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Parthasarathy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. R. Wallach
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. A. Wolf
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The first, third and fourth authors have been supported in part by NSF Grants #MCS-8300793, #MCS-7903153 and #MCS-8200235 respectively.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Enright, T.J., Parthasarathy, R., Wallach, N.R. et al. Unitary derived functor modules with small spectrum. Acta Math. 154, 105–136 (1985). https://doi.org/10.1007/BF02392820

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392820

Keywords

Search

Navigation