Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-559fc8cf4f-s5ss2 Total loading time: 0.496 Render date: 2021-03-06T09:28:57.175Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Canadian Journal of Mathematics Canadian Journal of Mathematics

Article contents

Decomposition of Splitting Invariants in Split Real Groups

Published online by Cambridge University Press:  20 November 2018

Tasho Kaletha
Tasho Kaletha
Affiliation:
University of Chicago, Chicago, IL 60637 USA email: tkaletha@math.uchicago.edu
Corresponding
E-mail address:
tkaletha@math.uchicago.edu
Save pdf (0.26 mb)
Rights & Permissions[Opens in a new window]

Abstract

For a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad constructed a cohomological invariant called the splitting invariant, which is an important component of their endoscopic transfer factors. We study this invariant in the case of a split real group and prove a decomposition theorem which expresses this invariant for a general torus as a product of the corresponding invariants for simple tori. We also show how this reduction formula allows for the comparison of splitting invariants between different tori in the given real group.

Keywords

11F70 22E47 11S37 11F72 17B22 endoscopy real lie group splitting invariant transfer factor
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 5 , 18 October 2011 , pp. 1083 - 1106
Copyright
Copyright © Canadian Mathematical Society 2011

References

[1] Agaoka, Y. and E. Kaneda, Strongly orthogonal subsets in root systems. Hokkaido Math. J. 31(2002), no. 1, 107–136.Google Scholar
[2] Bourbaki, N., Lie groups and Lie algebras. Springer-Verlag, Berlin, 2002.CrossRefGoogle Scholar
[3] Kaletha, T., Endoscopic character identities for depth-zero supercuspidal L-packets. arXiv:0909.1533v1.CrossRefGoogle Scholar
[4] Langlands, R. P., Orbital integrals on forms of SL(3). I. Amer. J. Math. 105(1983), no. 2, 465–506. doi:10.2307/2374265Google Scholar
[5] Langlands, R. P. and D. Shelstad, On the definition of transfer factors. Math. Ann. 278(1987), no. 1-4, 219–271. doi:10.1007/BF01458070Google Scholar
[6] Langlands, R. P. and D. Shelstad, Descent for transfer factors. In: The Grothendieck Festschrift, Vol. II. Progr. Math. 87. Birkhäuser Boston, Boston, MA, 1990, pp. 485–563.Google Scholar
[7] Demazure, M. and A. Grothendieck, SGA III. Lecture Notes in Mathematics 151. Springer-Verlag, Berlin, 1970.Google Scholar
[8] Shelstad, D., Characters and inner forms of a quasi-split group over R. Compositio Math. 39(1979), no. 1, 11–45.Google Scholar
[9] Shelstad, D., Orbital integrals and a family of groups attached to a real reductive group. Ann. Sci. École Norm. Sup. 12(1979), no. 1, 1–31.Google Scholar
[10] Shelstad, D., Embeddings of L-groups. Canad. J. Math. 33(1981), no. 3, 513–558. doi:10.4153/CJM-1981-044-4Google Scholar
[11] Shelstad, D., L-indistinguishability for real groups. Math. Ann. 259(1982), no. 3, 385–430. doi:10.1007/BF01456950Google Scholar
[12] Shelstad, D., A formula for regular unipotent germs. Orbites unipotentes et reprèsentations, II. Astérisque No. 171-172 (1989), 275–277.Google Scholar
[13] Shelstad, D., Tempered endoscopy for real groups. I. Geometric transfer with canonical factors. In: Representation Theory of Real Reductive Lie Groups. Contemp. Math. 472. American Mathematical Society, Providence, RI, 2008, pp. 215–246.Google Scholar
[14] Shelstad, D., Tempered endoscopy for real groups. II. Spectral transfer factors. In: Automorphic Forms and the Langlands Program. Adv. Lect. Math. (ALM) 9. Int. Press, Somerville, MA, 2010, pp. 236–276.Google Scholar
[15] Shelstad, D., Tempered endoscopy for real groups. III. Inversion of transfer and L-packet structure. Represent. Theory 12(2008), 369–402. doi:10.1090/S1088-4165-08-00337-3Google Scholar
[16] Springer, T. A., Linear Algebraic Groups. Progress in Mathematics 9. Birkhäuser, Boston, MA, 1981.Google 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: 15 *
View data table for this chart

* Views captured on Cambridge Core between 20th November 2018 - 6th March 2021. This data will be updated every 24 hours.

Access
1 Cited by

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.

Decomposition of Splitting Invariants in Split Real Groups
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.

Decomposition of Splitting Invariants in Split Real Groups
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.

Decomposition of Splitting Invariants in Split Real Groups
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *