Skip to main content
SpringerLink
Log in

A classification of the unitary irreducible representations ofSU(N, 1)

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

All inequivalent continuous unitary irreducible representations ofS U(N, 1) (N≧2) have been determined and classified. The matrix elements of the infinitesimal generators realized on a certain Hilbert space have been derived. Representations of the groups\(\overline {SU(N,1)} \),S U(N, 1)/Z N+1,\(\overline {U(N,1)} \) andU(N, 1) are classified in a similar manner.

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

Similar content being viewed by others

References

  1. Bargmann, V.: Ann. Math.48, 568 (1947).

    Google Scholar 

  2. Ottoson, U.: Commun. Math. Phys.8, 228 (1968).

    Google Scholar 

  3. Biedenharn, L. C., J. Nuyts, andN. Straumann: Ann. Inst. Henri Poincaré, Vol. III, no. 1, p. 13, Section A. (1965).

    Google Scholar 

  4. Godement, R.: Trans. Am. Math. Soc.73, 496 (1952).

    Google Scholar 

  5. Stein, E. M.: In: High-energy physics and elementary particles (IAEA, Vienna, 1965), p. 563.

    Google Scholar 

  6. Baird, G. E., andL. G. Biedenharn: J. Math. Phys.4, 1449 (1963).

    Google Scholar 

  7. Gelfand, I. M., andM. L. Tseitlin: Doklady Akad. Nauk SSSR71, 825 (1950);Gelfand, I. M., R. A. Minlos, andZ. Ya. Shapiro: Representations of the rotation and Lorentz groups and their applications. Oxford: Pergamon Press 1963.

    Google Scholar 

  8. Gårding, L.: Proc. Nat. Acad. Sci. US33, 331 (1947);Harish-Chandra: Trans. Am. Math. Soc.75, 185 (1953); Am. J. Math. 78, 564 (1956);Nelson, E.: Ann. Math.70, 572 (1959);Dixmier, J.: Bull. Soc. Math. France89, 9 (1961).

    Google Scholar 

  9. Biedenharn, L. C.: In: Non-compact groups in particle physics, p. 23 (Ed:Yutzechow). New York: W. A. Benjamin Inc. (1966);Santilli, R. M.:Nuovo Cimento 51, 74 (1967);Chakrabarti, A.: A class of representations of theI U (n) algebra and deformation toU (n, 1). Preprint. Centre de Physique Théorique de l'Ecole Polytechnique — 17, rue Descartes — 75 Paris V-France.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Sven Hultins gata, Göteborg

    Ulf Ottoson

Authors
  1. Ulf Ottoson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ottoson, U. A classification of the unitary irreducible representations ofSU(N, 1). Commun.Math. Phys. 10, 114–131 (1968). https://doi.org/10.1007/BF01654236

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01654236

Keywords

Search

Navigation