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Spectral synthesis for coadjoint orbits of nilpotent Lie groups. (English) Zbl 1355.43006
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 $$G$$.

##### MSC:
 43A45 Spectral synthesis on groups, semigroups, etc. 43A20 $$L^1$$-algebras on groups, semigroups, etc. 22E25 Nilpotent and solvable Lie groups 22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
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