Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2103.02968 |
| Tags: |
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Inhaltsangabe:
- Let $G$ be a nilpotent, connected, simply connected Lie group with Lie algebra $\mathfrak g$, and $π$ a unitary representation of $G$. The goal is to prove that the wave front set of $π$ coincides with the asymptotic cone of the orbital support of $π$, i.e. $\mathrm{WF}(π)=\mathrm{AC}(\bigcup_{σ\in \mathrm{supp}(π)}\mathcal O_σ)$, where $\mathcal O_σ\subset i\mathfrak g^\ast$ is the coadjoint orbit associated to the irreducible unitary representation $σ\in \hat{G}$ by Kirillov.