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Spectral transfer for metaplectic groups. I. Local character relations. (English) Zbl 1409.22014
This paper puts forward the investigation of elliptic spectral endoscopic transfer for the metaplectic cover \(\tilde {Sp}(2n)\) of the symplectic group \(Sp(2n)\) over a local field of characteristic zero. This map, which is dual to the geometric transfer of orbital integrals, is expected to yield endoscopic character relations that describe the internal structure of L-packets.
In the present paper, a first step is taken by characterising the image of the transfer map in the non-Archimedean case, then reducing the spectral transfer to the case of cuspidal test functions by means of a simple stable trace formula. In the Archimedean case, the author shows how the character relations and the spectral transfer factors can be read off the work of Adams and Renard.

MSC:
22E50 Representations of Lie and linear algebraic groups over local fields
11F72 Spectral theory; trace formulas (e.g., that of Selberg)
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