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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 \(G\).

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.)
Full Text: DOI
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