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An invariant for unitary representations of nilpotent Lie groups. (English) Zbl 0618.22005
The authors define an invariant for irreducible unitary representations of an arbitrary simply-connected nilpotent Lie group G. The invariant i(\(\rho)\) for a representation \(\rho\) is an element of the real cohomology of the Lie algebra of G; it is motivated by the Godbillon-Vey class for foliations, is constructed using the coadjoint orbit \({\mathcal O}\) corresponding to \(\rho\) and has degree dim(\({\mathcal O})+1\). The class is computed in several examples and is shown to be invariant under products of the representation by multiplicative characters.
Reviewer: G.Andrzejczak

22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
22D10 Unitary representations of locally compact groups
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