TY - JOUR
T1 - On the support of quasi-invariant measures on infinite-dimensional grasssmann manifolds
AU - Pickrell, Doug
PY - 1987/5
Y1 - 1987/5
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
SN - 0002-9939
VL - 100
SP - 111
EP - 116
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 1
ER -