On the continuous series for affine sl(2,R)
  We construct the representations of affine sl(2,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 divergencies. We view our construction as a step towards a realization of the principal series representations of affine sl(2,R). 
Igor B. Frenkel, Anton M. Zeitlin
math.RT hep-th math.QA