Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-x5fd4 Total loading time: 0.326 Render date: 2021-03-04T11:09:43.658Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Transfert d’intégrales orbitales pour le groupe métaplectique

Published online by Cambridge University Press:  07 September 2010

Wen-Wei Li
Affiliation:
Institut de Mathématiques de Jussieu – Université Paris Diderot 7, 175 rue du Chevaleret, 75013 Paris, France (email: wenweili@math.jussieu.fr)
Rights & Permissions[Opens in a new window]

Abstract

We set up a formalism of endoscopy for metaplectic groups. By defining a suitable transfer factor, we prove an analogue of the Langlands–Shelstad transfer conjecture for orbital integrals over any local field of characteristic zero, as well as the fundamental lemma for units of the Hecke algebra in the unramified case. This generalizes prior work of Adams and Renard in the real case and serves as a first step in studying the Arthur–Selberg trace formula for metaplectic groups.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2010

References

[1]Adams, J., Lifting of characters on orthogonal and metaplectic groups, Duke Math. J. 92 (1998), 129178.CrossRefGoogle Scholar
[2]Adams, J., Barbasch, D., Paul, A., Trapa, P. and Vogan, D. A. Jr., Unitary Shimura correspondences for split real groups, J. Amer. Math. Soc. 20 (2007), 701751.CrossRefGoogle Scholar
[3]Hales, T. C., A simple definition of transfer factors for unramified groups, in Representation theory of groups and algebras, Contemporary Mathematics, vol. 145 (American Mathematical Society, Providence, RI, 1993), 109134.CrossRefGoogle Scholar
[4]Howard, T., Lifting of characters on p-adic orthogonal and metaplectic groups, PhD thesis, University of Maryland (2007).Google Scholar
[5]Kottwitz, R. E., Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), 365399.CrossRefGoogle Scholar
[6]Labesse, J.-P., Cohomologie, stabilisation et changement de base, Astérisque 257 (1999), with Appendix A by L. Clozel and J.-P. Labesse and Appendix B by L. Breen.Google Scholar
[7]Lam, T. Y., Introduction to quadratic forms over fields, Graduate Studies in Mathematics, vol. 67 (American Mathematical Society, Providence, RI, 2005).Google Scholar
[8]Langlands, R. P. and Shelstad, D., On the definition of transfer factors, Math. Ann. 278 (1987), 219271.CrossRefGoogle Scholar
[9]Langlands, R. and Shelstad, D., Descent for transfer factors, in The Grothendieck Festschrift, Volume II, Progress in Mathematics, vol. 87 (Birkhäuser, Boston, MA, 1990), 485563.Google Scholar
[10]Lion, G. and Perrin, P., Extension des représentations de groupes unipotents p-adiques. Calculs d’obstructions, in Noncommutative harmonic analysis and Lie groups (Marseille, 1980), Lecture Notes in Mathematics, vol. 880 (Springer, Berlin, 1981), 337356.CrossRefGoogle Scholar
[11]Lion, G. and Vergne, M., The Weil representation, Maslov index and theta series, Progress in Mathematics, vol. 6 (Birkhäuser, Boston, MA, 1980).CrossRefGoogle Scholar
[12]Maktouf, K., Le caractère de la représentation métaplectique et la formule du caractère pour certaines représentations d’un groupe de Lie presque algébrique sur un corps p-adique, J. Funct. Anal. 164 (1999), 249339.CrossRefGoogle Scholar
[13]Mœglin, C., Vignéras, M.-F. and Waldspurger, J.-L., Correspondances de Howe sur un corps p-adique, Lecture Notes in Mathematics, vol. 1291 (Springer, Berlin, 1987).CrossRefGoogle Scholar
[14]Mœglin, C. and Waldspurger, J.-L., Décomposition spectrale et séries d’Eisenstein : une paraphrase de l’écriture, Progress in Mathematics, vol. 113 (Birkhäuser, Basel, 1994).Google Scholar
[15]Ngô, B.-C., Le lemme fondamental pour les algèbres de Lie, Publ. Math. Inst. Hautes Études Sci. 111 (2010), 1169.CrossRefGoogle Scholar
[16]Perrin, P., Représentations de Schrödinger, indice de Maslov et groupe metaplectique, in Noncommutative harmonic analysis and Lie groups (Marseille, 1980), Lecture Notes in Mathematics, vol. 880 (Springer, Berlin, 1981), 370407.CrossRefGoogle Scholar
[17]Renard, D., Transfert d’intégrales orbitales entre Mp(2n,R) et SO(n+1,n), Duke Math. J. 95 (1998), 425450.CrossRefGoogle Scholar
[18]Renard, D., Endoscopy for Mp(2n,R), Amer. J. Math. 121 (1999), 12151243.CrossRefGoogle Scholar
[19]Savin, G., Local Shimura correspondence, Math. Ann. 280 (1988), 185190.CrossRefGoogle Scholar
[20]Schultz, J., Lifting of characters of  and SO1,2(Ffor F a nonarchimedean local field, PhD thesis, University of Maryland (1998).Google Scholar
[21]Shelstad, D., Tempered endoscopy for real groups. I. Geometric transfer with canonical factors, in Representation theory of real reductive Lie groups, Contemporary Mathematics, vol. 472 (American Mathematical Society, Providence, RI, 2008), 215246.CrossRefGoogle Scholar
[22]Thomas, T., The Maslov index as a quadratic space, Math. Res. Lett. 13 (2006), 985999.CrossRefGoogle Scholar
[23]Thomas, T., The character of the Weil representation, J. Lond. Math. Soc. (2) 77 (2008), 221239.CrossRefGoogle Scholar
[24]Thomas, T., The Weil representation and Cayley transform, Preprint (2008),http://www.maths.ed.ac.uk/∼jthomas7/texts/Weil2.pdf.Google Scholar
[25]Waldspurger, J.-L., Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés, Astérisque 269 (2001).Google Scholar
[26]Waldspurger, J.-L., L’endoscopie tordue n’est pas si tordue, Mem. Amer. Math. Soc. 194 (2008).Google Scholar
[27]Weil, A., Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143211.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 181 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 4th March 2021. This data will be updated every 24 hours.

Access

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Transfert d’intégrales orbitales pour le groupe métaplectique
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Transfert d’intégrales orbitales pour le groupe métaplectique
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Transfert d’intégrales orbitales pour le groupe métaplectique
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *