1999/10/21 by S. V. Lüdkovsky, S. V. Ludkovsky, Ludkovsky, S. V.
Computer Science · Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Representation Theory (math.RT) #Topological and Geometric Data Analysis #advanced mathematical theories #math.RT
paper · pdf · doi:10.48550/arxiv.math/9910110
38 pages, 0 figures
arxiv created 1999/10/21 · openalex publication_date 1999/10/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gaussian quasi-invariant measures on groups of diffeomorphisms and loop groups G relative to dense subgroups G' were constructed. In the non-Archimedean case the wider class of measures was investigated, than in the real case. The cases of Riemann and non-Archimedean manifolds were considered. This article is related with unitary representations of G' associated with Poisson measures on G\bf N and uses quasi-invariant measures on G from the previous works. Several groups are considered: (1) (a) diffeomorphisms and (b) loop groups of real manifolds, (2) (a) diffeomorphisms and (b) loop groups of non-Archimedean manifolds over local fields. Besides these four cases further the fifth and the sixth cases are considered: for (3) (a) real and (b) non-Archimedean groups of diffeomorphisms Diff(M) representations associated with Poisson measures on configuration spaces ΓM contained in products of manifolds M\bf N are investigated. Here the cases of infinite-dimensional Banach manifold M (3) (a), non-Archimdean locally compact and non-locally compact Banach manifolds (3) (b) are investigated.