Endoscopy and Gan-Gross-Prasad Conjectures (1665)
Endoscopie et conjectures de Gan-Gross-Prasad 
Dates: 13-24 June 2016 at CIRM (Marseille Luminy, France)

W.-T. Gan, B. Gross and D. Prasad have stated deep conjectures about branching laws for automorphic representations of classical groups. The local non-archimedean conjectures have been proven recently for orthogonal groups by J.-L. Waldspurger [7] for tempered representation and extended to non tempered generic representations with help of C. Moeglin [6], by using methods from endoscopy. The case of unitary groups has been treated for tempered representations by R. Beuzart-Plessis in the non-archimedean [2] and archimedean case [3]. For non generic representations, the situation is more complicate and further input from endoscopy is necessary. The aim of this Research in Pairs is to make some progress on this and related questions.

[1] W.-T. Gan, B. Gross, D. Prasad: Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups, Astérisque 346, pp. 1-109, 2012.
[2] R. Beuzart-Plessis, A local trace formula for the Gan-Gross-Prasad conjecture for unitary groups: the archimedean case, arXiv:1506.01452v1, 300 p., 2015.
[3] R. Beuzart-Plessis, Endoscopie et conjecture local raffinée de Gan-Gross-Prasad pour les groupes unitaires, Compos. Math, 151, pp. 1309-1371, 2015.
[4] V. Heiermann, Local Langlands Correspondence for Classical Groups and Affine Hecke Algebras, arXiv:1502.04357v2, 29 p., 2015.
[5] V. Heiermann, A note on Standard Modules and Vogan L-packets, arXiv:1504.04524v1, 10 p., 2015.           
[6] C. Moeglin, J.-L. Waldspurger, La conjecture locale de Gross-Prasad pour les groupes spéciaux orthogonaux: le cas général, Astérisque 347, pp. 167-216, 2012.
[7] J.-L. Waldspurger, La conjecture locale de Gross-Prasad pour les repréentations tempérées des groupes spéciaux orthogonaux, Astérisque 347, pp. 103-166, 2012.