English

Unitary representations of a loop ax+b group, Wiener measure and Gamma-function

Representation Theory 2012-10-09 v2 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

We construct a family of irreducible unitary representations of the loop affine group of a line (ax+b group) with central extension on the Hilbert space of square integrable functions with respect to the Wiener measure. We relate the matrix coefficients of the elements of the loop ax+b group to the loop analogue of the Gamma-function.

Keywords

Cite

@article{arxiv.1012.4826,
  title  = {Unitary representations of a loop ax+b group, Wiener measure and Gamma-function},
  author = {Anton M. Zeitlin},
  journal= {arXiv preprint arXiv:1012.4826},
  year   = {2012}
}

Comments

20 pages, minor revisions due to referees' comments, Journal of Functional Analysis, in press