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arXiv · 1301.4542

Matching of Hecke operators for Exceptional dual pair correspondences

Gordan Savin·Michael Woodbury
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Abstract

Let $\mathbf{G}$ be a split algebrac group of type $E_n$ defined over a $p$-adic field. This group contains a dual pair $G \times G'$ where one of the groups is of type $G_2$. The minimal representation of $\mathbf{G}$, 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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Gordan Savin, Michael Woodbury. 2013-01-23. Matching of Hecke operators for Exceptional dual pair correspondences. https://arxiv.org/abs/1301.4542

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