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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

On the support of quasi-invariant measures on infinite-dimensional Grassmann manifolds


Author: Doug Pickrell
Journal: Proc. Amer. Math. Soc. 100 (1987), 111-116
MSC: Primary 28C20; Secondary 58B25, 58C35
MathSciNet review: 883411
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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 $ {S^1} \to U(n,{\mathbf{C}})$, extends to this thickened Grassmannian, and the measure is quasiinvariant with respect to these point transformations.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0883411-3
PII: S 0002-9939(1987)0883411-3
Article copyright: © Copyright 1987 American Mathematical Society