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

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.

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

Cited by in corpus (2)

• On the unitary representations of the affine $ax+b$-group, $\widehat{sl}(2,\mathbb{R})$ and their relatives
• On the continuous series for affine sl(2,R)