On a correspondence between cuspidal representations of and
Authors:
David Ginzburg, Stephen Rallis and David Soudry
Journal:
J. Amer. Math. Soc. 12 (1999), 849907
MSC (1991):
Primary 11F27, 11F70, 11F85
Published electronically:
April 26, 1999
MathSciNet review:
1671452
Fulltext PDF Free Access
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Abstract: Let be an irreducible, automorphic, selfdual, 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, selfdual, 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.ohiostate.edu
David Soudry
Email:
soudry@math.tau.ac.il
DOI:
http://dx.doi.org/10.1090/S0894034799003008
PII:
S 08940347(99)003008
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
