Skip to main content

\(\bar \partial \)-Cohomology spaces associated with a certain group extension

  • 457 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 185)

Keywords

  • Unitary Representation
  • Haar Measure
  • Compact Subgroup
  • Discrete Series
  • Irreducible Unitary Representation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equations on complex manifolds, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 81–130.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. V. Bargman, On a Hilbert space of analytic functions and associated integral transform, I, Comm. Pure Appl. Math. 14 (1961) 187–214.

    CrossRef  MathSciNet  Google Scholar 

  3. Harish-Chandra, Representations of semisimple Lie groups, IV, Amer. J. Math. 77 (1955), 743–777; V, ibid. 78 (1956), 1–41; VI, ibid. 564–628.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Harish-Chandra, Discrete series for semisimple Lie groups, I, Acta Math. 115 (1965), 241–318; II, ibid. 116 (1966), 1–111.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. S. Kobayashi, Irreducibility of certain unitary representations, J. Math. Soc. Japan 20 (1968), 638–642.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Y. Matsushima and S. Murakami, On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds, Ann. of Math. (2) 78 (1963), 365–416.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Y. Matsushima and S. Murakami On certain cohomology groups attached to hermitian symmetric spaces, Osaka J. Math. 2 (1965), 1–35; II, ibid. 5 (1968), 223–241.

    MathSciNet  MATH  Google Scholar 

  8. S. Murakami, (a) Cohomology groups of vector-valued forms on symmetric spaces, Lecture notes at Univ. of Chicago, Summer 1966. (b) Facteurs d'automorphie associés à un espace hermitien symétrique, Geometry of homogeneous bounded domains, Centro Int. Mat. Estivo, 3° Ciclo, Urbino, 1967.

    Google Scholar 

  9. M. S. Narasimhan and K. Okamoto, An analogue of the Borel-Weil-Bott theorem for symmetric pairs of non-compact type, Ann. of Math. (2) 91 (1970), 486–511.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. K. Okamoto and H. Ozeki, On square-integrable \(\bar \partial \)-cohomology spaces attached to Hermitian symmetric spaces, Osaka J. Math. 4 (1967), 95–110.

    MathSciNet  MATH  Google Scholar 

  11. I. Satake, On unitary representations of a certain group extension (in Japanese), Sûgaku 21 (1969), 241–253.

    MathSciNet  Google Scholar 

  12. Fock representations and theta-functions, Proceedings of Conference on Riemann surface theory, Stony Brook, 1969.

    Google Scholar 

  13. W, Schmid, The conjecture of Langlands, Ann. of Math., to appear.

    Google Scholar 

  14. M. Shahshahani, Discontinuous subgroups of extensions of semi-simple Lie groups, Dissertation, University of California at Berkeley, 1970.

    Google Scholar 

  15. D. Shale, Linear symmetries of free boson fields, Trans. Amer. Math. Soc. 103 (1962), 149–167.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. A. Weil, Sur certains groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143–211.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1971 Springer-Verlag

About this paper

Cite this paper

Satake, I. (1971). \(\bar \partial \)-Cohomology spaces associated with a certain group extension. In: Horváth, J. (eds) Several Complex Variables II Maryland 1970. Lecture Notes in Mathematics, vol 185. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058769

Download citation

  • DOI: https://doi.org/10.1007/BFb0058769

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05372-9

  • Online ISBN: 978-3-540-36493-1

  • eBook Packages: Springer Book Archive