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Discrete degenerate representations of non-compact unitary groups

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Abstract

Two degenerate principal series of irreducible unitary representations of an arbitrary non-compact unitary groupU(p,1) are derived. These series are determined by the eigenvalues of the first and second-order invariant operators, which are shown to possess a discrete spectrum. The explicit form of the corresponding harmonic functions is derived and the properties of the discrete representations are discussed in detail. Moreover, in the Appendix, we derive the properties of the corresponding degenerate representations of an arbitrary compactU(p) group.

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Authors and Affiliations

  1. International Centre for Theoretical Physics, Trieste

    R. Rçaczka & J. Fischer

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  1. R. Rçaczka
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  2. J. Fischer
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On leave of absence from Institute of Nuclear Research, Warsaw, Poland.

On leave of absence from Institute of Physics of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia.

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Rçaczka, R., Fischer, J. Discrete degenerate representations of non-compact unitary groups. Commun.Math. Phys. 3, 233–257 (1966). https://doi.org/10.1007/BF01649523

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  • DOI: https://doi.org/10.1007/BF01649523

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