Measures on infinite dimensional Grassmann manifolds

Abstract

A 1-parameter family of quasi-invariant measures is presented. These measures are cylinder measures in graph coordinates. Their characteristic functions are represented as integrals relative to an infinite product measure. This is applied to the problem of determining the support properties of the measures. One of the measures can be used to define the unitary structure for the basic representation of the affine extension of the restricted unitary group. © 1987.