Transfert d'intégrales orbitales pour le groupe métaplectique

Details Transfert d'intégrales orbitales pour le groupe métaplectique Transfert d'intégrales orbitales pour le groupe métaplectique

2009-06-22

arxiv.org/abs/0906.4053v4

Compositio Math. 147 (2011), 524-590

Mathematics

Representation Theory

80 pages, some minor errors are corrected. Submitted

Scientific paper

10.1112/S0010437X10004963

This paper develops a formalism of endoscopy for the metaplectic group. We define the notions of stable conjugacy, elliptic endoscopic groups, correspondence of semisimple geometric conjugacy classes and the transfer factors in this setting, then we establish the transfer of antigenuine orbital integrals. Under the hypothesis that the residual characteristic of F is sufficiently large, the fundamental lemma for the units of the spherical Hecke algebra also holds. This generalizes the prior works of J. Adams and D. Renard for real metaplectic groups. Our approach is based on Harish-Chandra's descent method and the non-standard endoscopy on Lie algebras.

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