ITÔ–WIENER CHAOS AND THE HODGE DECOMPOSITION ON AN ABSTRACT WIENER SPACE
2013 ◽
Vol 16
(01)
◽
pp. 1350008
Keyword(s):
De Rham
◽
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.
1986 ◽
Vol 26
(2)
◽
pp. 191-202
◽
Keyword(s):
2006 ◽
Vol 13
(04)
◽
pp. 415-426
◽
Keyword(s):
2006 ◽
Vol 17
(1)
◽
pp. 1-26
◽
Keyword(s):
1950 ◽
Vol 2
◽
pp. 334-343
◽
Keyword(s):