Stabilization of the trace formula for metaplectic groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909150282252288 |
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| author | Li, Wen-Wei |
| author_facet | Li, Wen-Wei |
| contents | We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about the genuine $L^2$-automorphic spectrum, into a linear combination of stable trace formulas of products of split odd orthogonal groups via endoscopic transfer. By adapting the strategies of Arthur and Moeglin-Waldspurger from the linear case, the proof is built on a long induction process that mixes up local and global, geometric and spectral data. As a by-product, we also stabilize the local trace formula for metaplectic groups over any local field of characteristic zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06581 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stabilization of the trace formula for metaplectic groups Li, Wen-Wei Representation Theory Number Theory 11F72 (Primary) 11F27, 11F70 (Secondary) We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about the genuine $L^2$-automorphic spectrum, into a linear combination of stable trace formulas of products of split odd orthogonal groups via endoscopic transfer. By adapting the strategies of Arthur and Moeglin-Waldspurger from the linear case, the proof is built on a long induction process that mixes up local and global, geometric and spectral data. As a by-product, we also stabilize the local trace formula for metaplectic groups over any local field of characteristic zero. |
| title | Stabilization of the trace formula for metaplectic groups |
| topic | Representation Theory Number Theory 11F72 (Primary) 11F27, 11F70 (Secondary) |
| url | https://arxiv.org/abs/2109.06581 |