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Waldspurger's involution and lifting of characters


Authors: Stephen Devlin and Jason Schultz
Journal: Proc. Amer. Math. Soc. 135 (2007), 911-919
MSC (2000): Primary 22E50; Secondary 11F70
DOI: https://doi.org/10.1090/S0002-9939-06-08522-4
Published electronically: September 11, 2006
MathSciNet review: 2262890
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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 [Enhancements On Off] (What's this?)

  • [A] J. Adams, Characters of Covering Groups of $ SL(n)$, J. Inst. Math. Jussieu 2 (2003) no. 1, 1-21. MR 1955205 (2004a:22016)
  • [F] Y. Flicker, Automorphic Forms on Covering Groups of $ GL(2)$, Invent. Math. 57 (1980), 119-182. MR 0567194 (81m:10057)
  • [FK] Y. Flicker and D. Kazhdan, Metaplectic Correspondence, Inst. Hautes Études Sci. Publ. Math. 64 (1986), 53-110. MR 0876160 (88d:11049)
  • [G] 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)
  • [GHPS] S. Gelbart, R. Howe, and I. Piatetski-Shapiro, Uniqueness anand Existence of Whittaker Models for the Metaplectic Group, Israel. Jour. of Math. 34 (1979), nos. 1-2, 21-37. MR 0571393 (81j:22021)
  • [GPS1] 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)
  • [GPS2] S. Gelbart and I. Piatetski-Shapiro, Distinguished representations and modular forms of half-integral weight, Inv. Math. 59 (1980), 145-188. MR 0577359 (82b:10035)
  • [GPS3] 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)
  • [KP1] D.A. Kazhdan and S.J. Patterson, Metaplectic Forms, Publ. Math. I.H.E.S. 59 (1984), 35-142. MR 0743816 (85g:22033)
  • [KP2] D.A. Kazhdan and S.J. Patterson, Towards a Generalized Shimura Correspondence, Adv. in Math. 60(2) (1986), 161-234. MR 0840303 (87m:22050)
  • [LL] R.P. Langlands and J.-P. Labesse, L-indistinguishability for $ SL(2)$, Canad. J. Math. 31 (1979), 726-785. MR 0540902 (81b:22017)
  • [M] D. Manderscheid, Waldspurger's Involution and Types, J. London Math. Soc. (2) 70 (2004), no. 3, 567-585. MR 2096864 (2005j:11037)
  • [R] R. Ranga Rao, On some explicit formulas in the theory of Weil representations, Pac. J. Math 157 (1993), no. 2, 355-371. MR 1197062 (94a:22037)
  • [Sc] 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).
  • [W1] J.L. Waldspurger, Correspondence de Shimura, J. Math. Pures et Appl. 59 (1980), 1-133. MR 0577010 (83f:10029)
  • [W2] J.L. Waldspurger, Correspondence de Shimura et quaternions, Forum Math. 3 (1991), 219-307. MR 1103429 (92g:11054)
  • [We] A. Weil, Sur certaines groupes d'opérateurs unitaires, Acta Math. 11 (1964), 143-211. MR 0165033 (29:2324)

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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: https://doi.org/10.1090/S0002-9939-06-08522-4
Received by editor(s): February 14, 2005
Received by editor(s) in revised form: October 3, 2005
Published electronically: 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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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