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.
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