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

2012/10/31 by Igor B. Frenkel, Anton M. Zeitlin · 1 citation
Mathematics · Physics and Astronomy · #math.RT #hep-th #math.QA

paper · pdf · doi:10.1007/s00220-013-1832-9

published as Commun.Math.Phys. 326 (2014) 145-165 · 21 pages, v3: minor corrections

arxiv created 2014/03/08 · arxiv updated 2014/03/11

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).

Cited by

• On the unitary representations of the affine ax+b-group, \widehatsl(2,ℝ) and their relatives