Ingrid Beltita, Daniel Beltita
Representations of nilpotent Lie groups via measurable dynamical systems
(539K, ps)

ABSTRACT.  We study unitary representations associated to cocycles of measurable dynamical systems. Our main result establishes conditions on a cocycle, 
ensuring that ergodicity of the dynamical system under consideration 
is equivalent to irreducibility of its corresponding unitary representation. This general result is applied to some representations of finite-dimensional nilpotent Lie groups and to some representations of infinite-dimensional Heisenberg groups.