Skip to main content
Log in

Jordan algebras and generalized principal series representations

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

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

Instant access to the full article PDF.

References

  1. H. Braun and M. Koecher, Jordan-Algebren, Springer, Berlin Heidelberg New York, 1966

    Google Scholar 

  2. J. Faraut and A. Koranyi, Function spaces and reproducing kernels on bounded symmetric domains, J. Func. Anal.89 (1990), 64–89

    Google Scholar 

  3. S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, London 1978

    Google Scholar 

  4. S. Helgason, Groups and Geometric Analysis, Academic Press, London, 1984

    Google Scholar 

  5. R. Howe and E. Tan, Homogeneous Functions on Light Cones: the Infinitesimal Structure of Some Degenerate Principal Series Representations, Bull. Amer. Math. Soc.28 (1993), 1–74

    Google Scholar 

  6. R. Howe and T. Umeda, The Capelli identity, the double commutant theorem, and multiplicity free action. Math. Ann.290 (1991), 565–619

    Google Scholar 

  7. N. Jacobson, Structure and representations of Jordan algebras, Colloquium Publ., vol. 36, Amer. Math. Soc., Providence, Rhode Island, 1968

    Google Scholar 

  8. K.D. Johnson, Degenerate principal series and compact groups, Math. Ann.287 (1991), 703–718

    Google Scholar 

  9. K.D. Johnson, Degenerate principal series on tube type domains, Contemp. Math.138 (1992), 175–187

    Google Scholar 

  10. B. Kostant and S. Sahi, The Capelli Identity, Tube Domains, and the Generalized Laplace Transform, Adv. Math.87 (1991), 71–92

    Google Scholar 

  11. B. Kostant and S. Sahi, Jordan algebras and Capelli Identities, Invent. Math.112 (1993), 657–664

    Google Scholar 

  12. O. Loos, Bounded Symmetric Domains and Jordan Pairs, University of California, Irvine, 1977

    Google Scholar 

  13. B. Ørsted and G. Zhang, Generalized principal series representations and tube domains, Duke Math. J., to appear

  14. S. Sahi, Unitary representations on the Shilov boundary of a symmetric tube domain, Representations of Groups and Algebras (Contemp. Math. vol. 145), Am. Math. Soc., Providence, 1993

    Google Scholar 

  15. S. Sahi, Jordan algebras and degenerate principal series, to appear

  16. N.J. Vilenkin, Special functions and the theory of group representations, Transl. Math. Monographs, vol. 22, Amer. Math. Soc., Providence, Rhode Island, 1968

    Google Scholar 

  17. L. Vretare, Elementary spherical functions on symmetric spaces, Math. Scand.39 (1976), 343–358

    Google Scholar 

  18. D.P. Zelobenko, Compact Lie groups and their representations, Transl. Math. Monographs, vol. 40, Amer. Math. Soc., Providence, Rhode Island, 1973

    Google Scholar 

  19. G. Zhang, Some recurrence formulas for spherical polynomials on tube domains, to appear, Trans. Amer. Math. Soc.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, G. Jordan algebras and generalized principal series representations. Math. Ann. 302, 773–786 (1995). https://doi.org/10.1007/BF01444516

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444516

Mathematics Subject Classification (1991)

Navigation