The Gross–Prasad conjecture and local theta correspondence

By W. Gan, Atsushi Ichino. 2014

109 citations recorded by the source corpus.

We establish the Fourier–Jacobi case of the local Gross–Prasad conjecture for unitary groups, by using local theta correspondence to relate the Fourier–Jacobi case with the Bessel case established by Beuzart-Plessis. To achieve this, we prove two conjectures of Prasad on the precise description of the local theta correspondence for (almost) equal rank unitary dual pairs in terms of the local Langlands correspondence. The proof uses Arthur’s multiplicity formula and thus is one of the first examples of a concrete application of this “global reciprocity law”.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1f783463234bf3c97053911ee4394e73a14e9966

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In Geometry and Topology

1. Hiraku Atobe
2. W. Gan
3. Manjul Bhargava
4. Atsushi Ichino
5. Ralf Schmidt
6. Shuichiro Takeda

In Mathematical Physics

1. Hiraku Atobe
2. W. Gan
3. Atsushi Ichino
4. Manjul Bhargava
5. Shuichiro Takeda
6. Ralf Schmidt
7. Michael Rapoport

Citations in the corpus

• Local theta correspondence of tempered representations and Langlands parameters (2016, methodology): “akeda [GT1] and Gan–Savin [GS]. In the proofs of some of these results, the doubling see-saw diagram plays a crucial role. In addition, Problems A and B in the almost equal rank case were resolved in [GI2] for the unitary case and [At] for symplectic-orthogonal case by the local intertwining relatio”