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A Theta Lift for Spin7

Published online by Cambridge University Press:  04 December 2007

Nadya Gurevich
Nadya Gurevich
Affiliation:
Department of Mathematics, The Weizmann Institute of Science, Rehovoth 76100, Israel. e-mail: gur@wisdom.weizmann.ac.il
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Abstract

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We establish an example of a functorial lift from generic cuspidal representations of a similitude group of the type A1×C2 to generic representations of Spin7. Our construction uses the theta correspondence associated to the dual pair of the type (A1×C2B3) inside E7. We also consider another theta correspondence associated to the dual pair of type (A1×C2A1×A1) in D6 and show that these two pairs fit into a tower and the standard properties of a tower of theta correspondences hold.

Keywords

functorial liftingminimal representationtheta lifting.
Type
Research Article
Information
Compositio Mathematica , Volume 136 , Issue 1 , March 2003 , pp. 25 - 59
Copyright
© 2003 Kluwer Academic Publishers