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The fundamental lemma for $S\hbox {\lowercase {$p$}}(4)$

Author: Thomas C. Hales
Journal: Proc. Amer. Math. Soc. 125 (1997), 301-308
MSC (1991): Primary 22E50, 22E35, 20G25
MathSciNet review: 1346977
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Abstract: The fundamental lemma is a conjectural identity between the orbital integrals on two reductive groups. The fundamental lemma is required for the stabilization of the trace formula and for various applications to automorphic forms. This paper proves the fundamental lemma for the group $Sp(4)$ and its endoscopic groups.

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  • [A] M. Assem, Unipotent orbital integrals of spherical functions on $p$-adic $4\times 4$ symplectic groups, preprint.
  • [H1] T. Hales, Shalika Germs on $GSp(4)$, Astérisque 171-172 (1989), 195-256. MR 91g:22025
  • [H2] T. Hales, Orbital integrals on $U(3)$, The Zeta Function of Picard Modular Surfaces, Les Publications CRM, (R.P. Langlands and D. Ramakrishnan, eds.), 1992. MR 93d:22020
  • [H3] T. Hales, Unipotent representations and unipotent classes in $SL(n)$, Amer. J. Math. 115 (6) (1993), 1347-1383. MR 95a:22024
  • [H4] T. Hales, A simple definition of transfer factors for unramified groups, Contemporary Math 145 (1993), 109-134. MR 94e:22020
  • [H5] T. Hales, Twisted endoscopy of $GL(4)$ and $GL(5):$ transfer of Shalika germs, Duke Math. J. 76 (2) (1994), 595-632. MR 96f:22019
  • [H6] T. Hales, The fundamental lemma for standard endoscopy: reduction to unit elements, Canad. J. Math. 47 (1995), 974-994. MR 96g:22023
  • [K] D. Kazhdan, On lifting, Lie group representations, II, Lecture Notes in Math., vol 1041, Springer-Verlag, New York, 1984. MR 86h:22029
  • [Ko] R. Kottwitz, Stable trace formula: elliptic singular terms, Math. Ann. 275 (1986), 365-399. MR 88d:22027
  • [L] R. Langlands, Orbital integrals on forms of $SL(3)$, I, Amer. J. Math. 105 (1983), 465-506. MR 86d:22012
  • [LS1] R. Langlands, D. Shelstad, On principal values on $p$-adic manifolds, Lie Group Representations II, Lecture Notes in Math. vol 1041, Springer-Verlag, 1984. MR 86b:11082
  • [LS2] R. Langlands, D. Shelstad, On the definition of transfer factors, Math. Ann. 278 (1987), 219-271. MR 89c:11172
  • [LS3] R. Langlands, D. Shelstad, Descent for transfer factors, The Grothendieck festschrift, Progress in Math., Birkhäuser, 1990. MR 92i:22016
  • [S1] M. Schröder, Zählen der Punkte mod $p$ einer Shimuravarietät zu $GSp(4)$, thesis, Mannheim, 1993.
  • [S2] M. Schröder, Calculating $p$-adic orbital integrals on groups of symplectic similitudes in four variables, preprint.
  • [Wa1] J.-L. Waldspurger, Quelques résultats de finitude concernant les distributions invariantes sur les algèbres de Lie $p$-adiques, preprint.
  • [Wa2] J.-L. Waldspurger, Homogénéité de certaines distributions sur les groupes $p$-adiques, Inst. Hautes Études Sci. Publ. Math. 81 (1995), 25-72. CMP 96:04
  • [We] R. Weissauer, A special case of the fundamental lemma, Parts I, II, III, IV, preprints.

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Additional Information

Thomas C. Hales
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Received by editor(s): February 14, 1995
Received by editor(s) in revised form: July 21, 1995
Additional Notes: Research supported by the National Science Foundation.
Communicated by: Roe Goodman
Article copyright: © Copyright 1997 American Mathematical Society

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