Spectral synthesis for coadjoint orbits of nilpotent Lie groups

Abstract

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 $.

25 pages