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
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] Madan Lal Mehta, Random matrices, 2nd ed., Academic Press, Inc., Boston, MA, 1991. MR 1083764
  • [2] Doug Pickrell, Measures on infinite-dimensional Grassmann manifolds, J. Funct. Anal. 70 (1987), no. 2, 323–356. MR 874060, 10.1016/0022-1236(87)90116-9
  • [3] Graeme Segal and George Wilson, Loop groups and equations of KdV type, Inst. Hautes Études Sci. Publ. Math. 61 (1985), 5–65. MR 783348
  • [4] È. Pressli and G. Sigal, Gruppy petel, “Mir”, Moscow, 1990 (Russian). With an appendix by Segal and G. Wilson; Translated from the second English edition and with a preface by A. V. Zelevinskiĭ and A. O. Radul. MR 1071737
  • [5] Takeyuki Hida, Brownian motion, Applications of Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1980. Translated from the Japanese by the author and T. P. Speed. MR 562914
  • [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