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

2010/12/31 by Anton M. Zeitlin · 2 citations
Mathematics · Physics and Astronomy · #math.RT #hep-th #math-ph #math.MP

paper · pdf · doi:10.1016/j.jfa.2012.05.004

published as J. Funct. Anal. , Volume 263, Issue 3, pp. 529-548 (2012) · 20 pages, minor revisions due to referees' comments, Journal of Functional Analysis, in press

arxiv created 2012/05/05 · arxiv updated 2012/10/09

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.

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