On the support of quasi-invariant measures on infinite-dimensional Grassmann manifolds
Proc. Amer. Math. Soc. 100 (1987), 111-116
Primary 28C20; Secondary 58B25, 58C35
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Abstract: One antisymmetric analogue of Gaussian measure on a Hilbert space is a certain measure on an infinite-dimensional Grassmann manifold. The main purpose of this paper is to show that the characteristic function of this measure is continuous in a weighted norm for graph coordinates. As a consequence the measure is supported on a thickened Grassmann manifold. The action of certain unitary transformations, in particular smooth loops , extends to this thickened Grassmannian, and the measure is quasiinvariant with respect to these point transformations.
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