### 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 S^{1}→U(n, C), extends to this thickened Grassmannian, and the measure is quasiinvariant with respect to these point transformations.

Original language | English (US) |
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Pages (from-to) | 111-116 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 100 |

Issue number | 1 |

DOIs | |

State | Published - 1987 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**On the support of quasi-invariant measures on infinite-dimensional grasssmann manifolds.** / Pickrell, Douglas M.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - On the support of quasi-invariant measures on infinite-dimensional grasssmann manifolds

AU - Pickrell, Douglas M

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84968507706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968507706&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1987-0883411-3

DO - 10.1090/S0002-9939-1987-0883411-3

M3 - Article

AN - SCOPUS:84968507706

VL - 100

SP - 111

EP - 116

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -