ANALYSIS AND GEOMETRY ON MARKED CONFIGURATION SPACES

作者: Eugene Lytvynov , Yuri Kondratiev , Sergio Albeverio , Georgi Us

DOI:

关键词: Homogeneous spaceSemidirect productSymmetric spaceGeneralized flag varietyRiemannian manifoldMathematicsGeometryKlein geometryPrincipal homogeneous spaceGeneral linear group

摘要: We carry out analysis and geometry on a marked configuration space M over Riemannian manifold X with marks from M. suppose that is homogeneous of Lie group G. As transformation A we take the “lifting” to action ×M semidirect product Diff0(X) diffeomorphisms compact support G smooth currents, i.e., all C 1 mappings into which are equal identity +

参考文章(40)
M. Röckner, Yu. G. Kondratiev, S. Albeverio, Canonical dirichlet operator and distorted brownian motion on Poisson spaces Comptes rendus de l'Académie des sciences. Série 1, Mathématique. ,vol. 323, pp. 1179- 1184 ,(1996)
I. M. Gelfand, A. M. Veršik, M. I. Graev, Representations of the group of functions taking values in a compact Lie group Compositio Mathematica. ,vol. 42, pp. 217- 243 ,(1980)
I. M. Gelfand, M. I. Graev, A. M. Verťik, Representations of the group of smooth mappings of a manifold X into a compact Lie group Compositio Mathematica. ,vol. 35, pp. 299- 334 ,(1977)
Bruno Torrésani, Raphaël Høegh-Krohn, Sergio Albeverio, Jean Marion, Daniel Testard, Noncommutative Distributions: Unitary Representation of Gauge Groups and Algebras ,(1993)
E Lytvynov, S Albeverio, A Daletskii, Laplace operators and diffusions in tangent bundles over Poisson spaces arXiv: Probability. ,(2000)
Michael Röckner, Zhi-Ming Ma, Construction of diffusions on configuration spaces Osaka Journal of Mathematics. ,vol. 37, pp. 273- 314 ,(2000) , 10.18910/11049
Michael Röckner, Vladimir I. Bogachev, Nicolai V. Krylov, Elliptic regularity and essential self-adjointness of Dirichlet operators on $\mathbb {R}^n$ Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze. ,vol. 24, pp. 451- 461 ,(1997)
Hiroaki Shimomura, Poisson measures on the configuration space and unitary representations of the group of diffeomorphisms Journal of Mathematics of Kyoto University. ,vol. 34, pp. 599- 614 ,(1994) , 10.1215/KJM/1250518934