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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Waldspurger's involution and lifting of characters

Author(s): Stephen Devlin; Jason Schultz
Journal: Proc. Amer. Math. Soc. 135 (2007), 911-919.
MSC (2000): Primary 22E50; Secondary 11F70
Posted: September 11, 2006
MathSciNet review: 2262890
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Abstract | References | Similar articles | Additional information

Abstract: We show that Adams's $ L$-packet of discrete series representations of the two-fold metaplectic cover of $ SL_2$ coincides with Waldspurger's local near equivalence class.

References:

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Y. Flicker and D. Kazhdan, Metaplectic Correspondence, Inst. Hautes Études Sci. Publ. Math. 64 (1986), 53-110. MR 0876160 (88d:11049)

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S. Gelbart Weil's Representation and the Spectrum of the Metaplectic Group, Springer Lecture Notes in Mathematics, Vol. 530, Springer-Verlag (1976). MR 0424695 (54:12654)

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S. Gelbart and I. Piatetski-Shapiro, Some remarks on metaplectic cu cusp forms and the correspondences of Shimura and Waldspurger, Israel. Jour. of Math. 44 (1983), no. 2, 97-126. MR 0693355 (84g:10054)

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S. Gelbart and I. Piatetski-Shapiro, On Shimura's correspondence for modular forms of half-integral weight, Proc. Colloquium on Automorphic Forms, Representation Theory, and Arithmetic, Bombay, Tata Institute Research Studies in Mathematics 10, Springer-Verlag (1981). MR 0633657 (83b:10032)

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J. Schultz, Lifting of characters on $ \widetilde{SL}(2)$ and $ SO(1,2)$ over a non-archimedean local field, Ph.D. Thesis, University of Maryland (1998).

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Additional Information:

Stephen Devlin
Affiliation: Department of Mathematics, University of San Francisco, 2130 Fulton Street, San Francisco, California 94117
Email: smdevlin@usfca.edu

Jason Schultz
Affiliation: Office of the Chief Actuary, Social Security Administration, Baltimore, Maryland 21235

DOI: 10.1090/S0002-9939-06-08522-4
PII: S 0002-9939(06)08522-4
Received by editor(s): February 14, 2005
Received by editor(s) in revised form: October 3, 2005
Posted: September 11, 2006
Additional Notes: This article was co-authored by Jason Schultz in his private capacity. No official support or endorsement by the Social Security Administration or the United States is intended or should be inferred.
Communicated by: Dan M. Barbasch
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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