Endoscopic decomposition of characters of certain cuspidal representations
Authors:
David Kazhdan and Yakov Varshavsky
Journal:
Electron. Res. Announc. Amer. Math. Soc. 10 (2004), 11-20
MSC (2000):
Primary 22E50; Secondary 22E35
DOI:
https://doi.org/10.1090/S1079-6762-04-00125-8
Published electronically:
March 4, 2004
MathSciNet review:
2048427
Full-text PDF Free Access
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Additional Information
Abstract: We construct an endoscopic decomposition for local $L$-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.
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[KP]KP D. Kazhdan and A. Polishchuk, Generalization of a theorem of Waldspurger to nice representations, in The orbit method in geometry and physics (Marseille, 2000), 197–242, Progr. Math. 213, Birkhäuser, Boston, 2003.
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[De]De P. Deligne, Les corps locaux de caractéristique $p$, limites de corps locaux de caractéristique $0$, in Représentations des groupes réductifs sur un corps local, pp. 119–157, Hermann, Paris, 1984.
[DL]DL P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), 103–161.
[HC]HC Harish-Chandra, Harmonic analysis on reductive $p$-adic groups (Notes by G. van Dijk), Lecture Notes in Mathematics 162, Springer-Verlag, Berlin-New York, 1970.
[Ka1]Ka1 D. Kazhdan, Proof of Springer’s hypothesis, Israel J. Math. 28 (1977), 272–286.
[Ka2]Ka2 D. Kazhdan, On lifting, in Lie group representations, II (College Park, Md., 1982/1983), 209–249, Lecture Notes in Mathematics 1041, Springer, Berlin, 1984.
[Ka3]Ka3 D. Kazhdan, Representations of groups over close local fields, J. Analyse Math. 47 (1986), 175–179.
[KP]KP D. Kazhdan and A. Polishchuk, Generalization of a theorem of Waldspurger to nice representations, in The orbit method in geometry and physics (Marseille, 2000), 197–242, Progr. Math. 213, Birkhäuser, Boston, 2003.
[Ko1]Ko1 R. E. Kottwitz, Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 (1984), 611–650.
[Ko2]Ko2 R. E. Kottwitz, Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), 365–399.
[La1]La R. P. Langlands, Les débuts d’une formule des traces stable, Publ. Math. Univ. Paris VII 13, Paris, 1983.
[La2]La2 R. P. Langlands, Representations of abelian algebraic groups, Pacific J. Math. 1997, Special Issue, 231–250.
[Wa]Wa J.-L., Waldspurger, Transformation de Fourier et endoscopie, J. Lie Theory 10 (2000), 195–206.
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Additional Information
David Kazhdan
Affiliation:
Institute of Mathematics, Hebrew University, Givat-Ram, Jerusalem, 91904 Israel
MR Author ID:
99580
Email:
kazhdan@math.huji.ac.il
Yakov Varshavsky
Affiliation:
Institute of Mathematics, Hebrew University, Givat-Ram, Jerusalem, 91904 Israel
MR Author ID:
638793
Email:
vyakov@math.huji.ac.il
Keywords:
Endoscopy,
Deligne-Lusztig representations
Received by editor(s):
September 18, 2003
Received by editor(s) in revised form:
January 19, 2004
Published electronically:
March 4, 2004
Additional Notes:
The work of the second author was supported by the Israel Science Foundation (Grant No. 38/01-1)
Communicated by:
Svetlana Katok
Article copyright:
© Copyright 2004
American Mathematical Society
