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On Relative Trace Formulae: the Case of Jacquet-Rallis

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Abstract

We give an account of recent works on Jacquet-Rallis’ approach to the Gan-Gross-Prasad conjecture for unitary groups. We report on the present state of the Jacquet-Rallis relative trace formulae and on some current applications of it. We give also a precise computation of the constant that appears in the statement “Fourier transform and transfer commute up to a constant”.

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Notes

  1. Since it may be a source of confusion, we emphasize that it is f(a, t) in the expression below and not f(t, a).

  2. For a better result see the very recent preprint [10].

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Acknowledgements

I would like to thank the organizers of the VIASM Annual Meeting 2017 for the invitation to give a lecture and to offer me the opportunity to write this article for the proceedings. I would also like to thank them and especially Ngô Bao Châu for the wonderful stay in Vietnam.

During the preparation of this article, I received partial support from Institut Universitaire de France and Agence Nationale pour la Recherche (projects Ferplay ANR-13-BS01-0012 and Vargen ANR-13-BS01-0001-01).

I also thank Michał, Zydor for numerous discussions on the topics of the present article.

Finally, I thank Hang Xue for helpful correspondence. I thank the anonymous referee for her/his careful proofreading.

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  1. Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris Diderot (Paris 7) et Institut Universitaire de France, UMR 7586, Bâtiment Sophie Germain, Case 7012, F-75205, Paris Cedex 13, France

    Pierre-Henri Chaudouard

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Lecture at the Annual Meeting 2017 of the Vietnam Institute for Advanced Study in Mathematics

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Chaudouard, PH. On Relative Trace Formulae: the Case of Jacquet-Rallis. Acta Math Vietnam 44, 391–430 (2019). https://doi.org/10.1007/s40306-018-00312-3

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