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- Title
ITÔ-WIENER CHAOS AND THE HODGE DECOMPOSITION ON AN ABSTRACT WIENER SPACE.
- Authors
YANG, YUXIN
- Abstract
Using the structure of the Boson-Fermion Fock space and an argument taken from [P. Bieliavsky, M. Cahen, S. Gutt, J. Rawnsley and L. Schwachhofer, Symplectic connections, Int. J. Geom. Meth. Mod. Phys. 3 (2006) 375-420], we give a new proof of the triviality of the L2 cohomology groups on an abstract Wiener space, alternative to that given by Shigekawa [De Rham-Hodge-Kodaira's decomposition on an abstract Wiener space, J. Math. Kyoto. Univ. 26(2) (1986) 191-202]. We apply the representation theory of the symmetric group to characterize the spaces of exact and co-exact forms in their Boson-Fermion Fock space representation.
- Subjects
STRUCTURAL analysis (Engineering); PROOF theory; INTERACTING boson-fermion models; TOPOLOGICAL spaces; WIENER integrals; REPRESENTATIONS of algebras; CHAOS theory; MATHEMATICAL decomposition; COHOMOLOGY theory
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2013, Vol 16, Issue 1, p-1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025713500082