• DOI:10.1063/1.533149
• Corpus ID: 14976492

The character of the exceptional series of representations of SU(1,1)

@article{Basu1999TheCO,
  title={The character of the exceptional series of representations of SU(1,1)},
  author={Debabrata Basu and Subrata Bal and K. V. Shajesh},
  journal={Journal of Mathematical Physics},
  year={1999},
  volume={41},
  pages={461-467}
}

• D. Basu, S. Bal, K. V. Shajesh
• Published 9 June 1999
• Mathematics
• Journal of Mathematical Physics

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 Hσ 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 nonlocal metric appearing in the scalar product with respect to which the representations are unitary. Since the nonlocal 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 Hσ. 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.