Matching of Hecke operators for exceptional dual pair correspondences

JOURNAL OF NUMBER THEORY

卷:146

Article

Savin, Gordan¹  Woodbury, Michael² 

[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

[2] Columbia Univ, Dept Math, New York, NY 10027 USA

关键词: Hecke operators;    Dual pairs;   

DOI  :  10.1016/j.jnt.2013.07.002

来源: Elsevier

【 摘 要 】

Let G be a split algebraic group of type E defined over a p-adic field. This group contains a dual pair G x G' where one of the groups is of type G(2). The minimal representation of G, when restricted to the dual pair, gives a correspondence of representations of the two groups in the dual pair. We prove a matching of spherical Hecke algebras of G and G', when acting on the minimal representation. This implies that the correspondence is functorial, in the sense of Arthur and Langlands, for spherical representations. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free