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Wiener functionals on spaces of lie álgebra valued 1-currents, and unitary representations of current groups.
Marion, Jean

Data: 1989
Resum: Well-known results about Brownian and Wiener functionals on abstract Wiener spaces are extended to Wiener functionals on the space of g- valued 1-currents on a manifold X, where g is the Lie algebra of a compact semisimple Lie group G. We introduce a family of Shigekawa-Sobolev spaces of generalized Wiener functionals and on each of them one gets a regular representation of the current group D(X,G) of G-valued and compactly supported smooth mappings on X. Then, a kind of Weyl's construction is used to associate, to each Riemannian flag of X, a ring of non located and order I unitary representations of D(X, G) including the energy representations studied in [23], [14].
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 33 n. 1 (1989) p. 99-121, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_33189_08

21 p, 563.2 KB

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