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Special representations of nilpotent Lie groups and the associated Poisson representations of current groups
Current group canonical representation special representation
2012/4/18
In this paper we describe the new model of the representations of the current groups with a semisimple Lie group of the rank one. In the earlier papers of 70-80-th (Araki, Gelfand-Graev-Vershik) had p...
Banach representations and affine compactifications of dynamical systems
affine compactification affine flow Asplund space enveloping semigroup non-sensitivity right topological semigroup
2012/4/18
To every Banach space V we associate a compact right topological affine semigroup E(V). We show that a separable Banach space V is Asplund if and only if E(V) is metrizable, and it is Rosenthal (i.e. ...
Generic representations of abelian groups and extreme amenability
Unitary representations measure-preserving actions Urysohn space extremely amenable group Polish group Baire category
2011/8/31
Abstract: If $G$ is a Polish group and $\Gamma$ is a countable group, denote by $\Hom(\Gamma, G)$ the space of all homomorphisms $\Gamma \to G$. We study properties of the group $\cl{\pi(\Gamma)}$ for...
Semigroup representations in holomorphic dynamics
Semigroup representations holomorphic dynamics
2010/12/7
We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show,with some examples, that representation theory of semigroups is ...