An invariant for unitary representations of nilpotent Lie groups (Q1089112)

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.