Communications in Mathematical Physics

, Volume 90, Issue 3, pp 353-372

First online:

The Casimir operators of inhomogeneous groups

  • M. ChaichianAffiliated withDepartment of High Energy Physics, University of Helsinki
  • , A. P. DemichevAffiliated withInstitute of Nuclear Physics, Moscow State University
  • , N. F. NelipaAffiliated withInstitute of Nuclear Physics, Moscow State University

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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.