Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-23T08:38:33.334Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Kottwitz-Shelstad normalization of transfer factors for automorphic induction for GLn

Published online by Cambridge University Press:  11 January 2016

Kaoru Hiraga  and
Atsushi Ichino
Kaoru Hiraga
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan, [email protected]
Atsushi Ichino
Affiliation:
Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan, [email protected]
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.

Automorphic induction for GLn is a case of endoscopic transfer, and its character identity was established by Henniart and Herb, up to a constant of proportionality. We determine this constant in terms of the Kottwitz-Shelstad normalization of transfer factors, which involves certain ε-factors.

Keywords

22E50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 208: Memorial Volume for Professor Hiroshi Saito , December 2012 , pp. 97 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

References

[1] Arthur, J. and Clozel, L., Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Ann. of Math. Stud. 120, Princeton University Press, Princeton, NJ, 1989.Google Scholar
[2] Artin, E. and Tate, J., Class Field Theory, AMS Chelsea Publishing, Providence, 2009.Google Scholar
[3] Harris, M. and Taylor, R., The Geometry and Cohomology of Some Simple Shimura Varieties, Ann. of Math. Stud. 151, Princeton University Press, Princeton, NJ, 2001.Google Scholar
[4] Henniart, G., La conjecture de Langlands locale pour GL(3), Mém. Soc. Math. Fr. (N.S.) 11–12, Math. Soc. Fr., Paris, 1984.Google Scholar
[5] Henniart, G., On the local Langlands conjecture for GL(n): The cyclic case, Ann. of Math. (2) 123 (1986), 145–203.CrossRefGoogle Scholar
[6] Henniart, G., Induction automorphe pour GL(n, ℂ), J. Funct. Anal. 258 (2010), 3082–3096.CrossRefGoogle Scholar
[7] Henniart, G. and Herb, R., Automorphic induction for GL(n) (over local non-Archimedean fields), Duke Math. J. 78 (1995), 131–192.CrossRefGoogle Scholar
[8] Henniart, G. and Lemaire, B., Intégrales orbitales tordues sur GL(n,F) et corps locaux proches: Applications, Canad. J. Math. 58 (2006), 1229–1267.CrossRefGoogle Scholar
[9] Henniart, G. and Lemaire, B., Formules de caractères pour l’induction automorphe, J. Reine Angew. Math. 645 (2010), 41–84.Google Scholar
[10] Henniart, G. and Lemaire, B., Changement de base et induction automorphe pour GLn en caractéristique non nulle, Mém. Soc. Math. Fr. (N.S.) 124, Math. Soc. Fr., Paris, 2011.Google Scholar
[11] Hiraga, K. and Saito, H., On L-packets for inner forms of SLn , Mem. Amer. Math. Soc. 215 (2012), no. 1013.Google Scholar
[12] Howe, R. E., Tamely ramified supercuspidal representations of Gln , Pacific J. Math. 73 (1977), 437–460.CrossRefGoogle Scholar
[13] Kottwitz, R. E. and Shelstad, D., Foundations of Twisted Endoscopy, Astérisque 255, Soc. Math. France, Paris, 1999.Google Scholar
[14] Labesse, J.-P. and Langlands, R. P., L-indistinguishability for SL(2), Canad. J. Math. 31 (1979), 726–785.CrossRefGoogle Scholar
[15] Langlands, R. P. and Shelstad, D., On the definition of transfer factors, Math. Ann. 278 (1987), 219–271.CrossRefGoogle Scholar
[16] Shahidi, F., On certain L-functions, Amer. J. Math. 103 (1981), 297–355.CrossRefGoogle Scholar
[17] Shahidi, F., Fourier transforms of intertwining operators and Plancherel measures for GL(n), Amer. J. Math. 106 (1984), 67–111.CrossRefGoogle Scholar
[18] Tate, J., “Number theoretic background” in Automorphic forms, representations and L-functions (Corvallis, Orea, 1977), Pt. 2, Proc. Sympos. Pure Math. 33, Amer. Math. Soc., Providence, 1979, 3–26.CrossRefGoogle Scholar
[19] Waldspurger, J.-L., Sur les intégrales orbitales tordues pour les groupes linéaires: un lemme fondamental, Canad. J. Math. 43 (1991), 852–896.CrossRefGoogle Scholar
[20] Waldspurger, J.-L., Le lemme fondamental implique le transfert, Compos. Math. 105 (1997), 153–236.CrossRefGoogle Scholar
[21] Waldspurger, J.-L., La conjecture locale de Gross-Prasad pour les représentations tempérées des groupes spéciaux orthogonaux, preprint, arXiv:0911.4568 [math.RT].Google Scholar