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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2103.02968 |
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| _version_ | 1866912032064798720 |
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| author | Budde, Julia Weich, Tobias |
| author_facet | Budde, Julia Weich, Tobias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_02968 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Wave Front Sets of Nilpotent Lie Group Representations Budde, Julia Weich, Tobias Representation Theory Analysis of PDEs 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. |
| title | Wave Front Sets of Nilpotent Lie Group Representations |
| topic | Representation Theory Analysis of PDEs |
| url | https://arxiv.org/abs/2103.02968 |