Spectral synthesis for coadjoint orbits of nilpotent Lie groups (Q343645)

For a connected and simply connected nilpotent Lie group \(G\) and \(\pi\) an irreducible unitary representation of \(G\), \(\pi\) defines an irreducible unitary representation of the convolution algebra \(L^1(G)\). In the paper under review, the authors determine the space of primary ideals in \(L^1(G)\) by identifying for every \(\pi\) the family \(\mathcal{I}^\pi\) of primary ideals with hull \(\{\pi\}\), with a family of invariant subspaces of a certain finite dimensional subspace of the space of polynomials on \(G\).