Abstract:
This article contains a survey of results on representations of the diffeomorphism group of a noncompact manifold X associated with the space Γx of configurations (that is, of locally finite subsets) in X. These representations are constructed from a quasi-invariant measure μ on Γx. In particular, necessary and sufficient conditions are established for the representations to be irreducible. In the case of the Poisson measure μ a description is given of the corresponding representation ring.
\Bibitem{VerGelGra75}
\by A.~M.~Vershik, I.~M.~Gel'fand, M.~I.~Graev
\paper Representations of the group of diffeomorphisms
\jour Russian Math. Surveys
\yr 1975
\vol 30
\issue 6
\pages 1--50
\mathnet{http://mi.mathnet.ru/eng/rm4288}
\crossref{https://doi.org/10.1070/RM1975v030n06ABEH001527}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=399343}
\zmath{https://zbmath.org/?q=an:0317.58009|0337.58003}
Linking options:
https://www.mathnet.ru/eng/rm4288
https://doi.org/10.1070/RM1975v030n06ABEH001527
https://www.mathnet.ru/eng/rm/v30/i6/p3
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