Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1987-0883411-3
MathSciNet review: 883411
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] M. L. Mehta, Random matrices, Academic Press, New York, 1967. MR 1083764 (92f:82002)
  • [2] D. Pickrell, Measures on infinite dimensional Grassmann manifolds, J. Funct. Anal. (to appear). MR 874060 (88d:58017)
  • [3] G. Segal and G. Wilson, Loop groups and equations of KdV type, Inst. Haute Étude Sci. Publ. Math. No. 61, 1985, p. 5. MR 783348 (87b:58039)
  • [4] G. Segal and A. Pressley, Representations of loop groups, Oxford Univ. Press (to appear). MR 1071737 (92a:22024)
  • [5] T. Hida, Brownian motion, Springer-Verlag, 1980. MR 562914 (81a:60089)
  • [6] Pierre de la Harpe, Classical Banach Lie algebras and groups, Lecture Notes in Math., vol. 285, Springer-Verlag, Berlin and New York, 1972.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 28C20, 58B25, 58C35

Retrieve articles in all journals with MSC: 28C20, 58B25, 58C35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0883411-3
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society