Communications in Mathematical Physics

, Volume 90, Issue 3, pp 353–372

The Casimir operators of inhomogeneous groups


  • M. Chaichian
    • Department of High Energy PhysicsUniversity of Helsinki
  • A. P. Demichev
    • Institute of Nuclear PhysicsMoscow State University
  • N. F. Nelipa
    • Institute of Nuclear PhysicsMoscow State University

DOI: 10.1007/BF01206887

Cite this article as:
Chaichian, M., Demichev, A.P. & Nelipa, N.F. Commun.Math. Phys. (1983) 90: 353. doi:10.1007/BF01206887


We have found the number of invariant operators for the inhomogeneous groups IGL(n, R), ISL(n, R), ISO(p, q), IU(p, q), ISU(p, q), ISp(2n), i.e. the inhomogeneous groups with the classical homogeneous subgroups, and also for the Weyl group W(p, q). For some special cases explicit forms of the invariant operators are obtained. We also discuss the methods applied, together with problems in some cases, possible further developments and relevance for the supersymmetric theories.

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© Springer-Verlag 1983