Invariant measures and orbit closures for unipotent actions on homogeneous spaces. (English) Zbl 0801.22008
A survey paper concerning mainly the author’s results about the action of a unipotent subgroup \(U\) of a connected Lie group \(G\) on a homogeneous space \(G/\Gamma\), where \(\Gamma\) is a discrete subgroup of \(G\). The results were published in a series of papers beginning in 1990. Some new extensions, as well as applications to ergodic theory and number theory, are also discussed.
Reviewer: A.L.Onishchik (Yaroslavl)
MSC:
| 22E40 | Discrete subgroups of Lie groups |
| 28D20 | Entropy and other invariants |
| 43A85 | Harmonic analysis on homogeneous spaces |
| 22D40 | Ergodic theory on groups |
| 43A05 | Measures on groups and semigroups, etc. |
| 53C30 | Differential geometry of homogeneous manifolds |
Keywords:
action; unipotent subgroup; connected Lie group; homogeneous space; discrete subgroup; ergodic theoryReferences:
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