Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T04:23:56.628Z Has data issue: false hasContentIssue false
  • English
  • Français

Matching of Weighted Orbital Integrals for Metaplectic Correspondences

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 prove an identity between weighted orbital integrals of the unit elements in the Hecke algebras of $\text{GL}\left( r \right)$ and its $n$-fold metaplectic covering, under the assumption that $n$ is relatively prime to any proper divisor of every $1\,\le \,j\,\le \,r$.

Keywords

22E35
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 4 , 01 December 2001 , pp. 482 - 490
Copyright
Copyright © Canadian Mathematical Society 2001

References

[1] Arthur, J., The trace formula in invariant form. Ann. of Math. 114 (1981), 1–74.Google Scholar
[2] Arthur, J., The invariant trace formula I. Local theory. J. Amer. Math. Soc. 1 (1988), 323–383.Google Scholar
[3] Arthur, J., The local behaviour of weighted orbital integrals. Duke Math. J. 56 (1988), 223–293.Google Scholar
[4] Flicker, Y., Automorphic forms on covering groups of GL(2). Invent.Math. 57 (1980), 119–182.Google Scholar
[5] Flicker, Y., On the symmetric square. Unit elements. Pacific J. Math. 175 (1996), 507–526.Google Scholar
[6] Flicker, Y. and Kazhdan, D., Metaplectic correspondence. Inst. Hautes Études Sci. Publ. Math. 64 (1986), 53–110.Google Scholar
[7] Kazhdan, D., On Lifting. In: Lie group representations II, Lecture Notes in Math. 1041, Springer-Verlag, 1984, 209–249.Google Scholar
[8] Kazhdan, D. and Patterson, S.,Metaplectic forms. Inst. Hautes Études Sci. Publ. Math. 59 (1984), 35–142.Google Scholar
[9] Kazhdan, D. and Patterson, S., Towards a generalized Shimura correspondence. Adv. in Math. 60 (1986), 161–234.Google Scholar
[10] Lang, S., Algebra. Addison-Wesley, 1993.Google Scholar
[11] Mezo, P., A Global Comparison for General Linear Groups and their Metaplectic Coverings. PhD thesis, University of Toronto, 1998.Google Scholar
[12] Mezo, P., New identities in the Harmonic Analysis of complex general linear groups. Preprint.Google Scholar