On The Continuous Series for sl(2,R)^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\widehat{sl(2,{\mathbb{R}})}}}$$\end{document}

We construct the representations of sl(2,R)^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widehat{sl(2,\mathbb{R})}}$$\end{document} 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 sl(2,R)^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\widehat{sl(2,\mathbb{R})}}$$\end{document}.