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
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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.
-  Madan Lal Mehta, Random matrices, 2nd ed., Academic Press, Inc., Boston, MA, 1991. MR 1083764
-  Doug Pickrell, Measures on infinite-dimensional Grassmann manifolds, J. Funct. Anal. 70 (1987), no. 2, 323–356. MR 874060, https://doi.org/10.1016/0022-1236(87)90116-9
-  Graeme Segal and George Wilson, Loop groups and equations of KdV type, Inst. Hautes Études Sci. Publ. Math. 61 (1985), 5–65. MR 783348
-  È. Pressli and G. Sigal, \cyr 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
-  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
-  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.