Geodesic
Finite factor representations of 2-step nilpotent groups, and orbit theory
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 120-140

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In this paper we describe factor representations of discrete 2-step nilpotent groups with 2-divisible center. We show that some standard theorems of the orbit theory are valid in the case of these groups. For countable 2-step nilpotent groups, we explain how to construct a factor representation starting from the orbit of the “coadjoint representation.” We also prove that every factor representation (more precisely, every trace) can be obtained by this construction, and prove a theorem on the decomposition of the factor representation restricted to a subgroup. 
@article{ZNSL_2004_307_a3,
     author = {K. P. Kokhas'},
     title = {Finite factor representations of 2-step nilpotent groups, and orbit theory},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {120--140},
     publisher = {mathdoc},
     volume = {307},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a3/}
}
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K. P. Kokhas'. Finite factor representations of 2-step nilpotent groups, and orbit theory. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part X, Tome 307 (2004), pp. 120-140. http://geodesic.mathdoc.fr/item/ZNSL_2004_307_a3/