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Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups

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Abstract

We propose an approach, via relative trace formulae, toward the global restriction problem involving Bessel or Fourier–Jacobi periods on unitary groups \({{\rm U}_n \times {\rm U}_m}\) , generalizing the work of Jacquet–Rallis for m = n − 1 (which is a Bessel period). In particular, when m = 0, we recover a relative trace formula proposed by Flicker concerning Kloosterman/Fourier integrals on quasi-split unitary groups. As evidences for our approach, we prove the vanishing part of the fundamental lemmas in all cases, and the full lemma for \({{\rm U}_n \times {\rm U}_n}\) .

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  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Yifeng Liu

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Liu, Y. Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups. manuscripta math. 145, 1–69 (2014). https://doi.org/10.1007/s00229-014-0666-x

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