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The Character of the Exceptional Series of Representations of SU(1,1)

Debabrata Basu·Subrata Bal·K. V. Shajesh
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Abstract

The character of the exceptional series of representations of SU(1,1) is determined by using Bargmann's realization of the representation in the Hilbert space $H_σ$ of functions defined on the unit circle. The construction of the integral kernel of the group ring turns out to be especially involved because of the non-local metric appearing in the scalar product with respect to which the representations are unitary. Since the non-local metric disappears in the `momentum space' $i.e.$ in the space of the Fourier coefficients the integral kernel is constructed in the momentum space, which is transformed back to yield the integral kernel of the group ring in $H_σ$. The rest of the procedure is parallel to that for the principal series treated in a previous paper. The main advantage of this method is that the entire analysis can be carried out within the canonical framework of Bargmann.

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Debabrata Basu, Subrata Bal, K. V. Shajesh. 1999-06-09. The Character of the Exceptional Series of Representations of SU(1,1). https://doi.org/10.1063/1.533149

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