A Theta Lift for Spin7

Nadya Gurevich

doi:10.1023/A:1022610116617

A Theta Lift for Spin₇

Nadya Gurevich

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We establish an example of a functorial lift from generic cuspidal representations of a similitude group of the type A₁ × C ₂ to generic representations of Spin₇. Our construction uses the theta correspondence associated to the dual pair of the type (A ₁ × C₂, B₃) inside E₇. We also consider another theta correspondence associated to the dual pair of type (A₁ × C₂, A₁ × A₁) in D₆ and show that these two pairs fit into a tower and the standard properties of a tower of theta correspondences hold.

Original language	English
Pages (from-to)	25-59
Number of pages	35
Journal	Compositio Mathematica
Volume	136
Issue number	1
DOIs	https://doi.org/10.1023/A:1022610116617
State	Published - 1 Mar 2003
Externally published	Yes

Keywords

Functorial lifting
Minimal representation
Theta lifting

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1023/A:1022610116617

Cite this

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abstract = "We establish an example of a functorial lift from generic cuspidal representations of a similitude group of the type A1 × C 2 to generic representations of Spin7. Our construction uses the theta correspondence associated to the dual pair of the type (A 1 × C2, B3) inside E7. We also consider another theta correspondence associated to the dual pair of type (A1 × C2, A1 × A1) in D6 and show that these two pairs fit into a tower and the standard properties of a tower of theta correspondences hold.",

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