1210.2135 (Igor B. Frenkel et al.)

On the continuous series for $\hat{sl(2,\mathbb{R})}$    [PDF]

Igor B. Frenkel, Anton M. Zeitlin

We construct the representations of $\hat{sl(2,\mathbb{R})}$ 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 divergencies. We view our construction as a step towards a realization of the principal series representations of $\hat{sl(2,\mathbb{R})}$.

View original: http://arxiv.org/abs/1210.2135