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Spectral transfer for metaplectic groups. I. Local character relations

Wen-Wei Li Chinese Academy of Sciences

Representation Theory mathscidoc:1703.29001

Distinguished Paper Award in 2017

Journal of the Institute of Mathematics of Jussieu, 2016.12
Let Mp(2n) be the metaplectic covering of Sp(2n) over a local field of characteristic zero. The core of the theory of endoscopy for Mp(2n) is the geometric transfer of orbital integrals to its elliptic endoscopic groups. The dual of this map, called the spectral transfer, is expected to yield endoscopic character relations which should reveal the internal structure of L-packets. As a first step, we characterize the image of the collective geometric transfer in the non-archimedean case, then reduce the spectral transfer to the case of cuspidal test functions by using a simple stable trace formula. In the archimedean case, we establish the character relations and determine the spectral transfer factors by rephrasing the works by Adams and Renard.
endoscopy; character relation; metaplectic group; Arthur–Selberg trace formula
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  • To appear in JIMJ. http://dx.doi.org/10.1017/S1474748016000384
@inproceedings{wen-wei2016spectral,
  title={Spectral transfer for metaplectic groups. I. Local character relations},
  author={Wen-Wei Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170314222015583983709},
  booktitle={Journal of the Institute of Mathematics of Jussieu},
  year={2016},
}
Wen-Wei Li. Spectral transfer for metaplectic groups. I. Local character relations. 2016. In Journal of the Institute of Mathematics of Jussieu. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170314222015583983709.
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