On a correspondence between cuspidal

representations of and

Authors:
David Ginzburg, Stephen Rallis and David Soudry

Journal:
J. Amer. Math. Soc. **12** (1999), 849-907

MSC (1991):
Primary 11F27, 11F70, 11F85

DOI:
https://doi.org/10.1090/S0894-0347-99-00300-8

Published electronically:
April 26, 1999

MathSciNet review:
1671452

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Abstract: Let be an irreducible, automorphic, self-dual, cuspidal representation of , where is the adele ring of a number field . Assume that has a pole at and that . Given a nontrivial character of , we construct a nontrivial space of genuine and globally -generic cusp forms on -the metaplectic cover of . is invariant under right translations, and it contains all irreducible, automorphic, cuspidal (genuine) and -generic representations of , which lift (``functorially, with respect to ") to . We also present a local counterpart. Let be an irreducible, self-dual, supercuspidal representation of , where is a -adic field. Assume that has a pole at . Given a nontrivial character of , we construct an irreducible, supercuspidal (genuine) -generic representation of , such that has a pole at , and we prove that is the unique representation of satisfying these properties.

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Additional Information

**David Ginzburg**

Affiliation:
School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Email:
ginzburg@math.tau.ac.il

**Stephen Rallis**

Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210

Email:
haar@math.ohio-state.edu

**David Soudry**

Email:
soudry@math.tau.ac.il

DOI:
https://doi.org/10.1090/S0894-0347-99-00300-8

Received by editor(s):
July 22, 1998

Received by editor(s) in revised form:
March 1, 1999

Published electronically:
April 26, 1999

Additional Notes:
The first and third authors’ research was supported by The Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.

Article copyright:
© Copyright 1999
American Mathematical Society