Geodesic
On the Fundamental Lemma for Standard Endoscopy: Reduction to Unit Elements
Canadian journal of mathematics, Tome 47 (1995) no. 5, pp. 974-994

Voir la notice de l'article provenant de la source Cambridge University Press

The fundamental lemma for standard endoscopy follows from the matching of unit elements in Hecke algebras. A simple form of the stable trace formula, based on the matching of unit elements, shows the fundamental lemma to be equivalent to a collection of character identities. These character identities are established by comparing them to a compact-character expansion of orbital integrals.
DOI : 10.4153/CJM-1995-051-5
Mots-clés : 22E50, 22E35, 20G25 
Hales, Thomas C. On the Fundamental Lemma for Standard Endoscopy: Reduction to Unit Elements. Canadian journal of mathematics, Tome 47 (1995) no. 5, pp. 974-994. doi: 10.4153/CJM-1995-051-5
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[Al] Arthur, J., A trace formula for reductive groups I, Duke Math. J. (4) 45(1978), 911–953. Google Scholar

[A2] Arthur, J., On elliptic tempered characters, Acta Math. (1) 171(1993), 73–138. Google Scholar

[B] Borel, A., Automorphic L-functions. In: Automorphic Forms, Representations and L-functions, Proc. Sympos. Pure Math. (2) 33, Amer. Math. Soc., Providence, Rhode Island, 1979. Google Scholar

[BJ] Borel, A. and Jacquet, H., Automorphic forms and automorphic representations. In: Automorphic Forms, Representations and L-functions, Proc. Sympos. Pure Math. (1) 33, Amer. Math. Soc, Providence, Rhode Island, 1979. Google Scholar

[C] Carter, R., Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, Wiley Interscience, New York, 1986. Google Scholar

[Cil] Clozel, L., Orbital integrals on p-adic groups: A proof of the Howe conjecture, Ann. of Math. (2) 129(1989), 237–251. Google Scholar

[CI2] Clozel, L., The fundamental lemma for stable base change, Duke Math. J. (1) 61(1990), 255–302. Google Scholar

[CD] Clozel, L. and Delorme, P., Le Théorème de Paley-Wiener invariantpour les groupes de Lie réductifs, Inv. Math. 77(1984), 427-453. Google Scholar

[G] Gérardin, P., Construction de séries discrètes p-adiques, Lecture Notes in Math. 462, Springer, 1975. Google Scholar

[HI] Hales, T.C., Unipotent Representations and Unipotent Classes in, SL(n), Amer. J. Math. (6) 115(1993), 1347–1383. Google Scholar

[H2] Hales, T.C., A Simple Definition of Transfer Factors for Unramified Groups, Contemp. Math. 145(1993), 109–134. Google Scholar

[He] Henniart, G., La conjecture de Langlands locale pour, GL(3), Mem. Soc. Math. France (N.S.) 11— 12(1984). Google Scholar

[Ka] Kazhdan, D., On Lifting. In: Lie Group Representations II, Lecture Notes in Math. 1041, 1984. Google Scholar

[Ke] Keys, D., Reducibility of Unramified Unitary Principal Series Representations of p-adic Groups and Class-1 Representations, Math. Ann. 259- 260(1982), 397–402. Google Scholar

[Kn] Knapp, A.W., Representation Theory of Semisimple Groups, Princeton, New Jersey, 1986. Google Scholar

[Kol] Kottwitz, R., Rational Conjugacy Classes in Reductive Groups, Duke Math. J. (4) 49(1982). Google Scholar

[Ko2] Kottwitz, R., Stable trace formula: cuspidal tempered terms, Duke Math. J. (3) 51(1984), 611–650. Google Scholar

[Ko3] Kottwitz, R., Stable Trace Formula: Elliptic Singular Terms, Math. Ann. 275(1986), 365–399. Google Scholar

[KR] Kottwitz, R. and Rogawski, J., The distributions in the invariant trace formula are supported on characters, preprint. Google Scholar

[KSI] Kottwitz, R. and Shelstad, D., Twisted Endoscopy I: Definitions, Norm Mappings and Transfer Factors, preprint. Google Scholar

[KS2] Kottwitz, R., Twisted Endoscopy II: Basic Global Theory, preprint. Google Scholar

[L] Langlands, R.P., Les débuts d'une formule des traces stable, Publ. Math. Univ. Paris VII, 1983. Google Scholar

[La] Labesse, J.-P., Fonctions élémentaires et lemme fondamental pour le changement de base stable, Duke Math. J. (2) 61(1990), 519–530. Google Scholar

[LSI] Langlands, R. and Shelstad, D., On the definition of transfer factors, Math. Ann. 278(1987), 219–271. Google Scholar

[LS2] Langlands, R., Descent for transfer factors. In: The Grothendieck festschrift, Progr. Math., Birkhäuser, 1990. Google Scholar

[M] MacDonald, I.G., Spherical Functions on a group of p-adic type, Ramanujan Institute, 1971. Google Scholar

[S] Sansuc, J.-J., Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres,, J. Reine Angew. Math. 327(1981), 12–80. Google Scholar

[Shl] Shelstad, D., Embeddings ofL-groups, Canad. J. Math. (3) 33(1981), 513–558. Google Scholar

[Sh2] Shelstad, D., Characters and Inner forms of a quasi-split group over ℝ, Compositio Math. (1) 39(1979), 11–45. Google Scholar

[Sh3] Shelstad, D., L-indistinguishability for Real Groups, Math. Ann. 259(1982), 385–430. Google Scholar

[Sh4] Shelstad, D., Orbital Integrals, Endoscopic Groups, and L-indistinguishability for Real Groups., In: Journées Automorphes, Publ. Math. Univ. Paris VII 15(1983), 135–219. Google Scholar

[Vi] Vignéras, M.-F., Caractérisation des intégrales orbitales sur un groupe réductifp-adique, J. Fac. Sci. Univ. Tokyo Sect 1A Math. 28(1981), 945–961. Google Scholar

[Vo] Vogan, D., Representations of Real Reductive Groups, Birkhäuser, Boston, 1981. Google Scholar

[W] Waldspurger, J.-L., Sur les intégrales orbitales tordues pour les groupes linéaires: un lemme fondamental,, Canad. J. Math.(4) 43(1991), 852–896. Google Scholar

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