Abstract
The reduction ofn-fold tensor products of induced unitary representations of noncompact groups into irreducible constituents is shown. Clebsch-Gordon coefficients are then calculated. The technique is applied to then-fold tensor products of the positive mass representations of the Poincaré group.
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References
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Our method rests mainly on what Mackey calls the subgroup theorem. We have not used the most general definition of induced representation. Further, measures defining Hilbert spaces and double cosets can be found in this reference. SeeMackey, G. W.: Theory of Group Representations. Dept of Mathematics, The University of Chicago. Chicago, Illinois 1955.
See, for example,Klink, W. H.: Preprint67–59, University of Iowa (1967).
Rideau: Ann. Insti. Henri Poincaré3, 339 (1965).
The fact that the inducing sugroups differ forn=2 andn ≧ 3 implies that the calculation of Clebsch-Gordan coefficients must be carried through separately for each case. We will consider onlyn ≧ 3. For the case,n=2, see reference 10.
Rohrlich, F.: Nuovo Cimento38, 673 (1965).
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Klink, W.H., Smith, G.J. On the reduction ofn-fold tensor product representations of noncompact groups. Commun.Math. Phys. 10, 231–244 (1968). https://doi.org/10.1007/BF01654233
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DOI: https://doi.org/10.1007/BF01654233