On the continuous series for affine sl(2,R)

TL;DR

This paper constructs representations of affine sl(2,R) by leveraging unitary representations of the loop ax+b-group, involving combinatorial analysis and renormalization, aiming to realize principal series representations.

Contribution

It introduces a novel method to build affine sl(2,R) representations from loop group representations, addressing divergencies through renormalization.

Findings

Successful construction of affine sl(2,R) representations

Analysis of correlation functions of generators

Framework for realizing principal series representations

Abstract

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).