• Corpus ID: 12395148

Restrictions of representations of classical groups: examples

@article{Gan2009RestrictionsOR,
  title={Restrictions of representations of classical groups: examples},
  author={Wee Teck Gan and B. Gross and Dipendra Prasad},
  journal={arXiv: Number Theory},
  year={2009}
}
In an earlier paper, we considered several restriction problems in the representation theory of classical groups over local and global fields. Assuming the Langlands-Vogan parameterization of irreducible representations, we formulated precise conjectures for the solutions of these restriction problems. In the local case, our conjectural answer is given in terms of Langlands parameters and certain natural symplectic root numbers associated to them. In the global case, the conjectural answer is… 
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References

SHOWING 1-10 OF 80 REFERENCES
Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
We consider several questions about restriction of representations of classical and metaplectic groups over local and global fields to subgroups, extending considerably the scope of the earlier work
Theta correspondence for unitary groups
In this paper we study the theta correspondence for Unitary groups ofthe same size over local and global fields. This correspondence has been studied in many cases by several authors. We are able to
From Laplace to Langlands via representations of orthogonal groups
In the late 1960s, Robert Langlands proposed a new and far-reaching connection between the representation theory of Lie groups over real and p-adic fields, and the structure of the Galois groups of
Generalised form of a conjecture of Jacquet and a local consequence
Abstract Following the work of Harris and Kudla, we prove a general form of a conjecture of Jacquet relating the non-vanishing of a certain period integral to non-vanishing of the central critical
Theta dichotomy for unitary groups
Some recent work of Gross and Prasad [14] suggests that the root numbers attached to certain symplectic representations of the Weil-Deligne group of a local field F control certain branching rules
Models for Certain Residual Representations of Unitary Groups
We dedicate this paper to Stephen Gelbart on the occasion of his 60th birthday Abstract. In this paper, we consider the generalized Gelfand-Graev mod- els for automorphic forms on unitary groups,
Endoscopy, theta-liftings, and period integrals for the unitary group in three variables
L-packets for the quasi-split unitary group in three variables U(3). We shall give an explicit parametrization of these L-packets using theta liftings and describe some relations between the
Depth-zero supercuspidal L-packets and their stability
In this paper we verify the local Langlands correspondence for pure inner forms of unramied p-adic groups and tame Langlands parameters in \general position". For each such parameter, we explicitly
Correspondances de Howe sur un corps p-adique
This book grew out of seminar held at the University of Paris 7 during the academic year 1985-86. The aim of the seminar was to give an exposition of the theory of the Metaplectic Representation (or
Howe Correspondence for Real Unitary Groups
Roger Howe proved that for any reductive dual pair (G, G′) in the symplectic groupSp(2n, R), there is a one-to-one correspondence of irreducible admissible representations of some two-fold covers
...
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