This paper concerns the problem of irreducibly decomposing unitary representations of the group of diffeomorphisms with compact support on the smooth manifold . As was shown in , these representations are decomposable under a fairly mild condition. In this paper, we consider a specific example of unitary representations that has been considered by . is already a factor representation of type ; in addition, it may be decomposed into irreducible components through the left regular representatation of the group of the finite permutations. We describe the concrete realization of these irreducible components. The results obtained herein have some resemblance to the finite-dimensional case of  with the exception of the factor representatation. In addition, we will give another proofs of the irreducibility and equivalence that were obtained by .
Cite this article
Hiroaki Shimomura, Unitary Representations of the Group of Diffeomorphisms via Restricted Product Measures with Infinite Mass II. Publ. Res. Inst. Math. Sci. 48 (2012), no. 1, pp. 183–213DOI 10.2977/PRIMS/66