Representations of filtered solvable Lie algebras (Q2884658)

The author studies the irreducible representations of filtered solvable algebras. It is proved that every such representation has the form of a representation induced by a Vergne polarization for some \(f\in\mathfrak{g}^\ast\). It is also proved that this map is a bijection if extended to equivalence classes of irreducible representations in this category. The article includes also the computation of spectra of representations induced from irreducible representations of subalgebras and the spectrum of the tensor product of two irreducible representations.