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

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

2010-12-21

arxiv.org/abs/1012.4826v1

Mathematics

Representation Theory

20 pages

Scientific paper

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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