Relative trace formulae toward Bessel and Fourier–Jacobi periods on unitary groups
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We propose an approach, via relative trace formulae, toward the global restriction problem involving Bessel or Fourier–Jacobi periods on unitary groups U[subscript n] × U[subscript 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 U[subscript n] × U[subscript n].
Date issued
2014-03Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Manuscripta Mathematica
Publisher
Springer Berlin Heidelberg
Citation
Liu, Yifeng. “Relative Trace Formulae toward Bessel and Fourier–Jacobi Periods on Unitary Groups.” Manuscripta Mathematica 145.1–2 (2014): 1–69.
Version: Author's final manuscript
ISSN
0025-2611
1432-1785