Imbedding of a~group of measure-preserving diffeomorphisms into a~semidirect product and its unitary representations

R. S. Ismagilov

Sbornik. Mathematics, Tome 41 (1982) no. 1, pp. 67-81

Résumé

The author considers the group $D^0(X,v)$ of diffeomorphisms of a compact manifold $X$ that preserve a measure $v$, and describes its unitary representations whose restrictions to any subgroup $D^0(Y,v)$, where $Y\simeq\mathbf R^n$, are continuous on $D^0(Y,v)$ with respect to convergence in measure in $D^0(Y,v)$. As an example, a family of representations $T^\alpha$ indexed by the nonzero elements $\alpha\in H^1(X,\mathbf R)$ is studied. Bibliography: 12 titles.