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SPECTRAL TRANSFER FOR METAPLECTIC GROUPS. I. LOCAL CHARACTER RELATIONS

Part of: Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  07 December 2016

Wen-Wei Li
Wen-Wei Li*
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 55, Zhongguancun donglu, 100190 Beijing, People’s Republic of China University of Chinese Academy of Sciences, 19A, Yuquan lu, 100049 Beijing, People’s Republic of China (wwli@math.ac.cn)
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Abstract

Let $\widetilde{\text{Sp}}(2n)$ be the metaplectic covering of $\text{Sp}(2n)$ over a local field of characteristic zero. The core of the theory of endoscopy for $\widetilde{\text{Sp}}(2n)$ 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.

Keywords

endoscopycharacter relationmetaplectic groupArthur–Selberg trace formula

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields
Secondary: 11F72: Spectral theory; Selberg trace formula
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 18 , Issue 1 , January 2019 , pp. 25 - 123
Copyright
© Cambridge University Press 2016 

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