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\hat 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 $.