Transfert d'intégrales orbitales pour le groupe métaplectique
Transfert d'intégrales orbitales pour le groupe métaplectique
摘要：
本文发展了一种形式主义的内窥镜检查的metoplectic组。在此基础上，定义了稳定共轭、椭圆内镜群、半单几何共轭类对应和转移因子等概念，建立了反真轨道积分的转移.在F的剩余特征充分大的假设下，球面Hecke代数单位的基本引理也成立。这推广了J. Adams和D.实亚群的Renard。我们的方法是基于Harish-Chandra的下降法和李代数上的非标准内窥镜。
英文摘要：
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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