Some local-global non-vanishing results for theta lifts from orthogonal groups

Author:
Shuichiro Takeda

Journal:
Trans. Amer. Math. Soc. **361** (2009), 5575-5599

MSC (2000):
Primary 11F27

DOI:
https://doi.org/10.1090/S0002-9947-09-04787-4

Published electronically:
April 10, 2009

MathSciNet review:
2515824

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Abstract: We, first, improve a theorem of B. Roberts which characterizes non-vanishing of a global theta lift from to in terms of non-vanishing of local theta lifts. In particular, we will remove all the Archimedean conditions imposed upon his theorem. Secondly, following Roberts, we will apply our theorem to theta lifting of low rank similitude groups. Namely we characterize the non-vanishing condition of a global theta lift from to in our improved setting. Also we consider non-vanishing conditions of a global theta lift from to and explicitly compute the lift when it exists.

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Additional Information

**Shuichiro Takeda**

Affiliation:
Department of Mathematics, University of Pennsylvania, 209 South 33rd St., Philadelphia, Pennsylvania 19104-6395

Address at time of publication:
Department of Mathematics, Purdue University, 150 N. University, West Lafayette, Indiana 47907

Email:
stakeda@math.upenn.edu, stakeda@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-09-04787-4

Keywords:
Automorphic representation,
theta correspondence,
theta lifting

Received by editor(s):
July 31, 2006

Received by editor(s) in revised form:
January 22, 2008

Published electronically:
April 10, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.