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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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {K. P. Kokhas'},
     title = {Finite factor representations of 2-step nilpotent groups, and orbit theory},
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     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/

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