Communications in Mathematical Physics

, Volume 6, Issue 3, pp 205–225 | Cite as

Analytic continuation of group representations. VI

  • Robert Hermann


The Gell-Mann formula for analytically continuing group representations is worked out explicitly for more cases than in previous work, and extended to certain pseudo-Riemannian symmetric spaces. The method of finding the asymptotic behavior of matrix elements of group representations introduced in Part V is developed in more detail and it is shown how it leads to new mathematical problems in the theory of dynamical systems and Hilbert space theory.


Neural Network Dynamical System Statistical Physic Hilbert Space Matrix Element 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962.Google Scholar
  2. 2.
    Hermann, R.: Lie groups for physicists. New York: W. A. Benjamin 1966.Google Scholar
  3. 3.
    —— The Gell-Man formula for representations of semisimple groups. Commun. Math. Phys.2, 155–164 (1966).Google Scholar
  4. 4.
    —— Analytic continuation of group representations. Commun. Math. Phys., Part I,2, 251–270 (1966); Part II,3, 53–74 (1966); Part III,3, 75–97 (1966), Parts IV and V to appear.Google Scholar
  5. 5.
    -- Some properties of representation of non-compact groups. Proc. of the Seminar on Elementary Particle Physics, International Center for Theoretical Physics, Trieste, 1965.Google Scholar
  6. 6.
    -- Differential geometry and the calculus of variations. New York: Academic Press to be published.Google Scholar
  7. 7.
    Kostant, B.: Lie group representations on polynomial rings. Am. J. Math.85, 327–404 (1963).Google Scholar
  8. 8.
    Nijenhuis, A., andR. Richardson: Deformation of homomorphisms of Lie groups and Lie algebras. To be published in Bull. Am. Math. Soc.Google Scholar

Copyright information

© Springer-Verlag 1967

Authors and Affiliations

  • Robert Hermann
    • 1
  1. 1.Stanford Linear Accelerator CenterStanford

Personalised recommendations