1012.4826 (Anton M. Zeitlin)

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

Anton M. Zeitlin

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.

View original: http://arxiv.org/abs/1012.4826