Relations between unitary representations of diffeomorphism groups and those of the infinite symmetric group or of related permutation groups (Q1380140)

The authors study the interrelations between unitary representations of two kinds of groups. One of them is the group \(G=\text{Diff}_0 (M)\) of diffeomorphisms with compact support on a manifold of class \(C^{(n)}\), \(1\leq n\leq\infty\), and the others are certain permutation groups \(S\) contained in the group \(\widetilde \Sigma_\infty\) of all permutations of the set \(N\) of natural numbers. In certain typical cases, the considered permutation groups \(S\) are equal to the infinite symmetric group \(\Sigma_\infty\) of all finite permutations or its standard subgroups.