Spectral synthesis for coadjoint orbits of nilpotent Lie groups

We determine the space of primary ideals in the group algebra $L^1(G)$ of a connected nilpotent Lie group by identifying for every $\pi \in \widehat{G}$ the family ${\mathcal{I}}^{\pi }$ of primary ideals with hull $\{\pi \}$ with the family of invariant polynomials of a certain finite dimensional subspace ${\mathcal{P}}_Q^{\pi }$ of the space of polynomials $\mathcal{P}(G)$ on $G$.