Motives with Galois Group of type : an Exceptional Theta-CorrespondenceG: an Exceptional Theta-Correspondence2: an Exceptional Theta-Correspondence

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In this paper, we study an exceptional theta correspondence, obtained by restricting the minimal automorphic representation of the adjoint group of type E7 and rank 3 over Q to the dual pair G × PGSp6. Here G is the anisotropic form of G2 over Q; using the correspondence, we lift certain automorphic forms on G to holomorphic cusp forms on PGSp6. This lifting provides the first step in a project to construct motives of rank 7 and weight O over Q with Galois group of type G2.

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