Hostname: page-component-857557d7f7-zv5th Total loading time: 0 Render date: 2025-11-22T23:16:59.580Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparisons of General Linear Groups and their Metaplectic Coverings I

Published online by Cambridge University Press:  20 November 2018

Paul Mezo
Paul Mezo*
Affiliation:
Max-Planck-Institut für Mathematik Bonn PB: 7280 D-53072 Bonn Germany, email: mezo@mpim-bonn.mpg.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prepare for a comparison of global trace formulas of general linear groups and their metaplectic coverings. In particular, we generalize the local metaplectic correspondence of Flicker and Kazhdan and describe the terms expected to appear in the invariant trace formulas of the above covering groups. The conjectural trace formulas are then placed into a form suitable for comparison.

Keywords

11F7011F7222E50

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 54 , Issue 1 , 01 February 2002 , pp. 92 - 137
Copyright
Copyright © Canadian Mathematical Society 2002

References

[AC89] Arthur, J. and Clozel, L., Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. Ann. of Math. Stud. 120, Princeton Univ. Press, Princeton, NJ, 1989.Google Scholar
[AH97] Adams, J. and Huang, J.-S., Kazhdan-Patterson lifting for GL(n, R). Duke Math J. 89 (1997), 423–444.Google Scholar
[Art81] Arthur, J., The trace formula in invariant form. Ann. of Math. 114 (1981), 1–74.Google Scholar
[Art86] Arthur, J., On a family of distributions obtained from orbits. Canad. J. Math. 38 (1986), 179–214.Google Scholar
[Art88a] Arthur, J., The invariant trace formula I. Local theory. J. Amer. Math. Soc. 1 (1988), 323–383.Google Scholar
[Art88b] Arthur, J., The invariant trace formula II. Global theory. J. Amer. Math. Soc. 1 (1988), 501–554.Google Scholar
[Art88c] Arthur, J., The local behaviour of weighted orbital integrals. Duke Math. J. 56 (1988), 223–293.Google Scholar
[Art89] Arthur, J., Intertwining operators and residues I. Weighted characters. J. Funct. Anal. (1) 84 (1989), 19–84.Google Scholar
[BDK86] Bernstein, J., Deligne, P. and Kazhdan, D., Trace Paley-Wiener theorem for reductive p-adic groups. J. Analyse Math. 47 (1986), 180–192.Google Scholar
[Cas93] Casselman, W., Introduction to the theory of admissible representations of p-adic reductive groups. Unpublished notes, 1974–1993.Google Scholar
[CD84] Clozel, L. and Delorme, P., Le Théorème de Paley-Wiener invariant pour les groupes de Lie réductifs. Invent. Math. 77 (1984), 427–453.Google Scholar
[CW] Clozel, L. and Waldspurger, J.-L., La formule de Plancherel pour les groupes p-adiques. Unpublished notes.Google Scholar
[Duf75] Duflo, M., Représentations irréductibles des groupes semi-simples complexes. In: Analyse Harmonique sur les Groupes de Lie, Lecture Notes in Math. 497, Springer-Verlag, 1975, 26–88.Google Scholar
[FK86] Flicker, Y. and Kazhdan, D., Metaplectic correspondence. Inst. Hautes Études Sci. Publ. Math. 64 (1986), 53–110.Google Scholar
[HC84] Harish-Chandra, , The plancherel formula for reductive p-adic groups. In: Collected Papers vol. IV, Springer-Verlag, 1984.Google Scholar
[Kna86] Knapp, A., Representation Theory of Semisimple Groups. Princeton University Press, Princeton, NJ, 1986.Google Scholar
[KP84] Kazhdan, D. and Patterson, S. J., Metaplectic forms. Inst. Hautes É tudes Sci. Publ. Math. 59 (1984), 35–142.Google Scholar
[KP86] Kazhdan, D. and Patterson, S. J., Towards a generalized Shimura correspondence. Adv. in Math. 60 (1986), 161–234.Google Scholar
[Lan70] Lang, S., Algebraic Number Theory. Addison-Wesley Publishing Company, 1970.Google Scholar
[Lan84] Lang, S., Algebra. Addison-Wesley, 1984.Google Scholar
[Mez98] Mezo, P., A Global Comparison for General Linear Groups and their Metaplectic Coverings. PhD thesis, University of Toronto, 1998.Google Scholar
[Mez00] Mezo, P., Comparisons of general linear groups and their metaplectic coverings II. Represent. Theory, to appear.Google Scholar
[Rog83] Rogawski, J., Representations of GL(n) and division algebras over a p-adic field. Duke Math J. 50 (1983), 161–196.Google Scholar
[Sha84] Shahidi, F., Fourier transforms of intertwining operators and plancherel measures for GL(n). Amer. J. Math. 106 (1984), 67–111.Google Scholar
[Sil78] Silberger, A., The Langlands quotient theorem for p-adic groups. Math. Ann. 236 (1978), 95–104.Google Scholar
[Sun97] Sun, H., Examples of metaplectic tensor products. Preprint, 1997.Google Scholar
[Vig81] Vignéras, M.-F., Caractérisation des intégrales orbitales sur un groupe réductif p-adique. J. Fac. Sci. Univ. Tokyo, Sect. IA 29 (1981), 945–962.Google Scholar