Geodesic
Representations of the group of diffeomorphisms
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 30 (1975) no. 6, pp. 1-50

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This article contains a survey of results on representations of the diffeomorphism group of a noncompact manifold $X$ associated with the space $\Gamma_x$ of configurations (that is, of locally finite subsets) in $X$. These representations are constructed from a quasi-invariant measure $\mu$ on $\Gamma_x$. In particular, necessary and sufficient conditions are established for the representations to be irreducible. In the case of the Poisson measure $\mu$ a description is given of the corresponding representation ring. 
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     title = {Representations of the group of diffeomorphisms},
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A. M. Vershik; I. M. Gel'fand; M. I. Graev. Representations of the group of diffeomorphisms. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 30 (1975) no. 6, pp. 1-50. http://geodesic.mathdoc.fr/item/RM_1975_30_6_a0/