JournalsprimsVol. 48, No. 1pp. 183–213

Unitary Representations of the Group of Diffeomorphisms via Restricted Product Measures with Infinite Mass II

  • Hiroaki Shimomura

    Tokyo, Japan
Unitary Representations of the Group of Diffeomorphisms via Restricted Product Measures with Infinite Mass II cover
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Abstract

This paper concerns the problem of irreducibly decomposing unitary representations of the group Diff0(M)\text{Diff}_0(M) of diffeomorphisms with compact support on the smooth manifold MM. As was shown in [19], these representations are decomposable under a fairly mild condition. In this paper, we consider a specific example of unitary representations (T,Diff0(M))(T,\text{Diff}_0(M)) that has been considered by [4]. (T,Diff0(M))(T,\text{Diff}_0(M)) is already a factor representation of type II\text{II}_\infty; in addition, it may be decomposed into irreducible components through the left regular representatation of the group S{\frak{S}}_\infty 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 [20] with the exception of the factor representatation. In addition, we will give another proofs of the irreducibility and equivalence that were obtained by [4].

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. 183–213

DOI 10.2977/PRIMS/66