Communications in Mathematical Physics

, Volume 21, Issue 4, pp 284–290 | Cite as

A multiplicity theorem for representations of inhomogeneous compact groups

  • H. D. Doebner
  • J. Tolar


The problem of finiteness of multiplicities of irreducible unitary representations of a compact subgroup is considered for decompositions of irreducible unitary representations of locally compact groups. A simple solution is found for inhomogeneous compact groups and for a physically interesting class of groups with a non-abelian radical.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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.
    Mackey, G.W.: Infinite-dimensional group representations. Bull. Am. Math. Soc.69, 628–686 (1963).Google Scholar
  2. 2.
    Harish-Chandra: Representations of semi-simple Lie groups I, II, III. Proc. Nat. Acad. Sci. (U.S.)37, 170–173, 362–365, 366–369 (1951).Google Scholar
  3. 3.
    —— Representations of semi-simple Lie groups I, II, III. Trans. Am. Math. Soc.75, 185–243 (1953);76, 26–65, 234–253 (1954).Google Scholar
  4. 4.
    Godement, R.: A theory of spherical functions I. Trans. Am. Math. Soc.73, 496–556 (1952).Google Scholar
  5. 5.
    Gel'fand, I.M., Graev, M.I., Pyatetskii-Shapiro, I.I.: Representation theory and automorphic functions, Vol. 6 of Generalized functions, Chap. I, Sec. 2.3. Philadelphia: W. B. Saunders Co. 1969.Google Scholar
  6. 6.
    Mackey, G. W.: The theory of induced representations. Lecture notes, (Chicago 1955) (mimeographed).Google Scholar
  7. 7.
    Smirnov, W.I.: Lehrgang der höheren Mathematik, Vol. V. Berlin: VEB Deutscher Verlag der Wissenschaften 1962.Google Scholar
  8. 8.
    Doebner, H. D., Melsheimer, O.: On limitable dynamical groups in quantum mechanics — I: General theory and spinless model. J. Math. Phys.9, 1638–1656 (1968).Google Scholar
  9. 9.
    Melsheimer, O.: A new Lie group for the scalarSU(3)-symmetric strong coupling theory. Nucl. Phys. B5, 479–491 (1968).Google Scholar
  10. 10.
    Stein, E.M.: A survey of representations of non-compact groups in: High-energy physics and elementary particles, p. 563–584 (Secs. 6 and 8) (IAEA, Vienna 1965).Google Scholar
  11. 11.
    Hausner, M., Schwartz, J.T.: Lie groups, Lie algebras. Part II.7. New York: Gordon and Breach Sci. Publ. 1968.Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • H. D. Doebner
    • 1
    • 2
    • 4
  • J. Tolar
    • 1
    • 2
    • 3
  1. 1.International Centre for Theoretical PhysicsTriesteItaly
  2. 2.the University of MarburgFed. Rep. Germany
  3. 3.Faculty of Nuclear ScienceCzech Technical UniversityPragueCzechoslovakia
  4. 4.Institut für theoretische PhysikTechnische Universität ClausthalClausthalGermany

Personalised recommendations