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On The Continuous Series for \({{\widehat{sl(2,{\mathbb{R}})}}}\)

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Abstract

We construct the representations of \({\widehat{sl(2,\mathbb{R})}}\) starting from the unitary representations of the loop ax + b-group. Our approach involves a combinatorial analysis of the correlation functions of the generators and renormalization of the appearing divergences. We view our construction as a step towards a realization of the principal series representations of \({\widehat{sl(2,\mathbb{R})}}\).

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Authors and Affiliations

  1. Department of Mathematics, Yale University, 10 Hilhouse ave., New Haven, CT, 06511, USA

    Igor B. Frenkel

  2. Department of Mathematics, Columbia University, 2990 Broadway, New York, NY, 10027, USA

    Anton M. Zeitlin

Authors
  1. Igor B. Frenkel
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  2. Anton M. Zeitlin
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Correspondence to Anton M. Zeitlin.

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Communicated by Y. Kawahigashi

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Frenkel, I.B., Zeitlin, A.M. On The Continuous Series for \({{\widehat{sl(2,{\mathbb{R}})}}}\) . Commun. Math. Phys. 326, 145–165 (2014). https://doi.org/10.1007/s00220-013-1832-9

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  • DOI: https://doi.org/10.1007/s00220-013-1832-9

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