Skip to main content
SpringerLink
Log in

The Gell-Mann formula for representations of semisimple groups

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

Abstract

A method for constructing representations of non-compact semisimple groups from representations of semidirect product groups is presented. Necessary and sufficient algebraic conditions for the method to work are given, and these are applied to cases of possible interest for the classification of elementary particles.

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

Bibliography

  1. Gel'fand, I. M., andN. Ya. Vilenkin: Generalized functions, vol. 4. New York: Academic Press 1964.

    Google Scholar 

  2. Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962.

    Google Scholar 

  3. Hermann, R.: Lie groups for physicists. New York: W. A. Benjamin Inc. 1965.

    Google Scholar 

  4. -- Some properties of representations of non-compact groups, to appear. Proceedings of the Seminar on Elementary Particle Physics, International Center for Theoretical Physics, Trieste, 1965

  5. -- Analytic continuation of group representation, to appear.

  6. Koranyi, A., andJ. A. Wolf: Realizations of hermitian symmetric spaces as generalized half-planes. Ann. Math.8, 265–288 (1965).

    Google Scholar 

  7. Wigner, E.: Unitary representations of the Lorentz group. Ann. Math.40, 149 (1939).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Argonne National Laboratory and Northwestern University, USA

    R. Hermann

Authors
  1. R. Hermann
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the Office of Naval Research, # NONR 3656 (09).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hermann, R. The Gell-Mann formula for representations of semisimple groups. Commun.Math. Phys. 2, 155–164 (1966). https://doi.org/10.1007/BF01773350

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01773350

Keywords

Search

Navigation