Measures on infinite dimensional Grassmann manifolds
The author presents a 1-parameter family of quasi-invariant measures, which are cylinder measures in graph coordinates on the Hilbert-Schmidt Grassmannian of an infinite-dimensional Hilbert space. Their characteristic functions are represented as integrals relative to an infinite product measure. Then, using the Grass-Sazonov theorem, the author finds 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.
scientific article; zbMATH DE number 4006589