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Equivariant cohomology, Fock space and loop groups. (English) Zbl 1100.58015
Summary: Equivariant de Rham cohomology is extended to the infinite-dimensional setting of a loop subgroup acting on a loop group, using Hida supersymmetric Fock space for the Weil algebra and Malliavin test forms on the loop group. The Mathai–Quillen isomorphism (in the BRST formalism of Kalkman) is defined so that the equivalence of various models of the equivariant de Rham cohomology can be established.
58J65Diffusion processes and stochastic analysis on manifolds
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22E67Loop groups and related constructions, group-theoretic treatment