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 $π\in\hat G$ the family ${\mathcal I}^π$ of primary ideals with hull $\{π\}$ with the family of invariant polynomials of a certain finite dimensional subspace ${\mathcal P}_Q^π$ of the space of polynomials ${\mathcal P}(G)$ on $G$.

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