Symplectic Local Root Numbers , Central Critical L-values , and Restriction Problems in the Representation Theory of Classical Groups

  title={Symplectic Local Root Numbers , Central Critical L-values , and Restriction Problems in the Representation Theory of Classical Groups},
  author={Benedict H. Gross and D. Kalyan Ravi Prasad},
We give a conjectural description of the restriction of an irreducible representation of a unitary group U(n) to a subgroup U(n − 1) over a local or global field. We formulate analogous conjectures for the restriction problem from U(n) to a subgroup U(m) (m < n) using Bessel and Fourier-Jacobi models, and also similar restriction problems for symplectic groups. The conjectures are analogs of those in [GP1] and [GP2] for the orthogonal groups. We verify these conjectures in certain low rank… CONTINUE READING
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