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Multiplicity one, local and global conjugacy

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Abstract

The issue of local and global conjugacy is closely related to the multiplicity one property in representation theory and the Langlands program. In this article we give first families of connected instances for SO2N where the multiplicity one fails in both aspects of representation theory and automorphic forms with certain assumptions on the Langlands functoriality.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Algebraic Number Theory) (Grant No. A010102-11671380), One Hundred Talents Program at Chinese Academy of Sciences, and Project supported by the National Basic Research Program of China (Grant No. 2013CB834202), National Science Foundation of USA (Grant No. DMS-9729992). In these years, the author benefits from series of important discussions with Dinakar Ramakrishnan. Also, the author is grateful for helpful comments from a lot of people such as Binyong Sun, Wee Teck Gan, Dihua Jiang, Ye Tian, during the writing of this article. Finally, the author thanks all the comments made by the referees.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Song Wang

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Song Wang

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  1. Song Wang
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Wang, S. Multiplicity one, local and global conjugacy. Sci. China Math. 63, 1029–1038 (2020). https://doi.org/10.1007/s11425-018-9382-0

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