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Uniqueness of twisted linear periods and twisted Shalika periods

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Abstract

Let k be a local field of characteristic zero. Let π be an irreducible admissible smooth representation of GL2n(k). We prove that for all but countably many characters χ’s of GLn(k) × GLn(k), the space of χ-equivariant(continuous in the archimedean case) linear functionals on π is at most one dimensional. Using this, we prove the uniqueness of twisted Shalika models.

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant No. 11501478). The second author was supported by National Natural Science Foundation of China (Grant Nos. 11525105, 11688101, 11621061 and 11531008). The authors thank Avraham Aizenbud for helpful email communications, and thank Dmitry Gourevitch for a critical bibliographical remark. They also thank the referees for helpful comments to improve the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Fulin Chen

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

    Binyong Sun

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

    Binyong Sun

Authors
  1. Fulin Chen
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  2. Binyong Sun
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Correspondence to Binyong Sun.

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Chen, F., Sun, B. Uniqueness of twisted linear periods and twisted Shalika periods. Sci. China Math. 63, 1–22 (2020). https://doi.org/10.1007/s11425-018-9502-y

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  • DOI: https://doi.org/10.1007/s11425-018-9502-y

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