Matching of Hecke operators for Exceptional dual pair correspondences

2013/01/19 by Gordan Savin, Savin, Gordan, Michael Woodbury +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1301.4542

openalex publication_date 2013/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a split algebrac group of type E_n defined over a p-adic field. This group contains a dual pair G × G' where one of the groups is of type G₂. 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.

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