Abstract
Let G be a split algebraic group of type En 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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