On the support of quasi-invariant measures on infinite-dimensional Grassmann manifolds
Proc. Amer. Math. Soc. 100 (1987), 111-116
Primary 28C20; Secondary 58B25, 58C35
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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 , extends to this thickened Grassmannian, and the measure is quasiinvariant with respect to these point transformations.
Lal Mehta, Random matrices, 2nd ed., Academic Press, Inc.,
Boston, MA, 1991. MR 1083764
Pickrell, Measures on infinite-dimensional Grassmann
manifolds, J. Funct. Anal. 70 (1987), no. 2,
874060 (88d:58017), http://dx.doi.org/10.1016/0022-1236(87)90116-9
Segal and George
Wilson, Loop groups and equations of KdV type, Inst. Hautes
Études Sci. Publ. Math. 61 (1985), 5–65. MR 783348
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
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
Pierre de la Harpe, Classical Banach Lie algebras and groups, Lecture Notes in Math., vol. 285, Springer-Verlag, Berlin and New York, 1972.
- M. L. Mehta, Random matrices, Academic Press, New York, 1967. MR 1083764 (92f:82002)
- D. Pickrell, Measures on infinite dimensional Grassmann manifolds, J. Funct. Anal. (to appear). MR 874060 (88d:58017)
- 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)
- G. Segal and A. Pressley, Representations of loop groups, Oxford Univ. Press (to appear). MR 1071737 (92a:22024)
- T. Hida, Brownian motion, Springer-Verlag, 1980. MR 562914 (81a:60089)
- Pierre de la Harpe, Classical Banach Lie algebras and groups, Lecture Notes in Math., vol. 285, Springer-Verlag, Berlin and New York, 1972.
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