Special unipotent representations of real classical groups: construction and unitarity
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2017
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909497833816064 |
|---|---|
| author | Barbasch, Dan Ma, Jia-Jun Sun, Binyong Zhu, Chen-Bo |
| author_facet | Barbasch, Dan Ma, Jia-Jun Sun, Binyong Zhu, Chen-Bo |
| contents | Let $G$ be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit $\check{\mathcal O}$ of $\check G$, the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We classify all special unipotent representations of $G$ attached to $\check{\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. When $\check{\mathcal O}$ has good parity in the sense of Moeglin, we construct all such representations of $G$ via the method of theta lifting. As a consequence of the construction and the classification, we conclude that all special unipotent representations of $G$ are unitarizable, as predicted by the Arthur-Barbasch-Vogan conjecture. We also determine precise structure of the associated cycles of special unipotent representations of $G$. The paper is the second in a series of two papers on the classification of special unipotent representations of real classical groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_05552 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Special unipotent representations of real classical groups: construction and unitarity Barbasch, Dan Ma, Jia-Jun Sun, Binyong Zhu, Chen-Bo Representation Theory 22E45, 22E46 Let $G$ be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit $\check{\mathcal O}$ of $\check G$, the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We classify all special unipotent representations of $G$ attached to $\check{\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. When $\check{\mathcal O}$ has good parity in the sense of Moeglin, we construct all such representations of $G$ via the method of theta lifting. As a consequence of the construction and the classification, we conclude that all special unipotent representations of $G$ are unitarizable, as predicted by the Arthur-Barbasch-Vogan conjecture. We also determine precise structure of the associated cycles of special unipotent representations of $G$. The paper is the second in a series of two papers on the classification of special unipotent representations of real classical groups. |
| title | Special unipotent representations of real classical groups: construction and unitarity |
| topic | Representation Theory 22E45, 22E46 |
| url | https://arxiv.org/abs/1712.05552 |