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

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Abstract

One antisymmetric analogue of Gaussian measure on a Hubert 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 S1→U(n, C), extends to this thickened Grassmannian, and the measure is quasiinvariant with respect to these point transformations.

Original languageEnglish (US)
Pages (from-to)111-116
Number of pages6
JournalProceedings of the American Mathematical Society
Volume100
Issue number1
DOIs
StatePublished - 1987

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Invariant Measure
Grassmann Manifold
Weighted Norm
Unitary transformation
Gaussian Measure
Hubert Space
Grassmannian
Antisymmetric
Characteristic Function
Analogue
Graph in graph theory

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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abstract = "One antisymmetric analogue of Gaussian measure on a Hubert 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 S1→U(n, C), extends to this thickened Grassmannian, and the measure is quasiinvariant with respect to these point transformations.",
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