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

2015/09/30 by Anton M. Zeitlin
Mathematics · Physics and Astronomy · #math.RT #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.1090/pspum/092

published as Proc. Symp. Pure Math. 92 (2016) 325-355 · 30 pages, to appear in "Proceedings of Southeastern Lie Theory Workshop Series 2012-2014", Proc. Symp. Pure Math., AMS, 2015; v2: final version

arxiv created 2015/10/15 · arxiv updated 2021/09/28

Abstract

This article focuses on two related topics: unitary representations of the loop ax+b-group and their relation to a loop version of the Γ-function and the construction of continuous series for the \widehatsl(2,ℝ)-algebra. Mainly this is a survey of some results from arXiv:1012.4826 , arXiv:1210.2135 alongside with the motivation for them both from the physical and mathematical points of view.

Citations

• Unitary representations of a loop ax+b group, Wiener measure and Gamma-function
• On the continuous series for affine sl(2,R)