Completeness of coherent state subsystems for nilpotent Lie groups

van Velthoven, Jordy Timo

Comptes Rendus. Mathématique, Tome 360 (2022) no. G7, pp. 799-808.

Let $G$ be a nilpotent Lie group and let $\pi$ be a coherent state representation of $G$. The interplay between the cyclicity of the restriction ${\pi |}_{\Gamma }$ to a lattice $\Gamma \le G$ and the completeness of subsystems of coherent states based on a homogeneous $G$-space is considered. In particular, it is shown that necessary density conditions for Perelomov’s completeness problem can be obtained via density conditions for the cyclicity of ${\pi |}_{\Gamma }$.

Classification : 22E27, 42C30, 42C40, 81R30

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