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.

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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 -