Ergodicity and mixing \(T\)-induced flows (Q2784527)

\(T\)-induced flows are generalizations of flows on homogeneous spaces, where \(T\) is a continuous action of a closed subgroup \(H\) of a connected (real) Lie group \(G\) on a finite measure space \(X\). The vertical action \(S\) of \(G\) on \(X\times G\) induces an action \(\text{Ind\,}T\) of \(G\) on the space of orbits of the diagonal action of \(H\) on \(X\times G\). The restriction of \(\text{Ind\,}T\) to a one-parameter subgroup of \(G\) is called the \(T\)-induced flow corresponding to this one-parameter subgroup. The author states without proof some results on ergodicity and mixing of \(T\)-induced flows; these are formulated in terms of corresponding results on certain \(T\)-invariant partitions. The corresponding analogues for an induced unitary representation are also true. Finally, the author states an analogue of the Mautner phenomenon for \(T\)-induced flows.