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Motives with Galois Group of type G$_2$: an Exceptional Theta-Correspondence

Published online by Cambridge University Press:  04 December 2007

BENEDICT H. GROSS
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, e-mail: gross@math.harvard.edu
GORDAN SAVIN
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, e-mail: savin@math.utah.edu
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Abstract

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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 E$_7$ and rank 3 over Q to the dual pair GxPGSp$_6$. Here G is the anisotropic form of G$_2$ over Q; using the correspondence, we lift certain automorphic forms on G to holomorphic cusp forms on PGSp$_6$. 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 G$_2$.

Type
Research Article
Copyright
© 1998 Kluwer Academic Publishers