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The Metaplectic Tensor Product as an Instance of Langlands Functoriality

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L-Functions and Automorphic Forms

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 10))

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Abstract

We interpret the metaplectic tensor product construction of Mezo for the genuine representations of the Kazhdan-Patterson covering groups in terms of the L-group formalism of Weissman.

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References

  1. Cai, Y.Q.: Fourier coefficients for theta representations on covers of general linear groups. Preprint. Available at http://arxiv.org/abs/1602.06614

  2. Gan, W.T., Gao, F.: The Langlands-Weissman program for Brylinski-Deligne extensions. Asterisque (to appear). Available at http://arxiv.org/pdf/1409.4039v1.pdf

  3. Kazhdan, D.A., Patterson, S.J.: Metaplectic forms. I.H.E.S. Publ. Math. 59, 35–142 (1984)

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  5. Mezo, P.: Metaplectic tensor products for irreducible representations. Pac. J. Math. 215(1), 85–96 (2004)

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  8. Weissman, M.: L-groups and parameters for covering groups. Asterisque (to appear). arXiv:1507.01042

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Acknowledgements

I thank Shuichiro Takeda for his suggestion to write up this note and for helpful discussions during the course of this work. This note was initially meant to be an appendix to [7], but it has become too lengthy for this purpose. I also thank Yuanqing Cai for bringing Theorem 3.26 of his paper [1] to my attention, as well as Fan Gao and Paul Mezo for their comments on the first draft of this note. Thanks are also due to the referee for a careful reading which caught many typos. This work is partially supported by a Singapore government MOE Tier Two grant MOE2016-T2-1-059 (R-146-000-233-112).

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    Wee Teck Gan

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  1. Wee Teck Gan
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Correspondence to Wee Teck Gan .

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Editors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, Germany

    Jan Hendrik Bruinier

  2. Mathematisches Institut, Universität Heidelberg, Heidelberg, Germany

    Winfried Kohnen

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Gan, W.T. (2017). The Metaplectic Tensor Product as an Instance of Langlands Functoriality. In: Bruinier, J., Kohnen, W. (eds) L-Functions and Automorphic Forms. Contributions in Mathematical and Computational Sciences, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-69712-3_6

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