Abstract
At the Williastown conference on harmonic analysis, R. Howe publicized two conjectures concerning the orbital integrals of functions on a reductive p-adic group and on its Lie algebra. He proved the Lie algebra case of the conjecture himself; recently we have proved the conjecture on the group, at least in zero characteristic [4c,4d].
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References
J. Arthur and L. Clozel, Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Annals of Math. Studies, Vol. 120, Princeton University Press, Princeton, New Jersey, 1989.
J. Bernstein, P-invariant distributions on GL(N) and the classification of unitary representations of GL(N) (non archimedian case), Lie Group Representations II, Lecture Notes in Math., Vol. 1041 (R. Herb, ed.), Springer-Verlag, Berlin-New York, 1984, pp. 50–102.
J. Bernstein, P. Deligne, and D. Kazhdan, Trace Paley-Wiener theorem for reductive, p-adic groups, J. Analyse Math. 47 (1986), 180–192.
L. Clozel, Sur une conjecture de Howe-I, Compositio Math. 56 (1985), 87–110.
L. Clozel, Characters of non-connected, p-adic reductive groups, Can. J. Math. 39 (1987), 149–167.
L. Clozel, Orbital integrals on p-adic groups: a proof of the Howe conjecture, Ann. of Math. 129 (1989), 237–251.
L. Clozel, The fundamental lemma for stable base change, Duke Math. J. 61 (1990), 255-302.
L. Clozel and P. Delorme, Le théorème de Paley-Wiener invariant pour les groupes de Lie réductifs II, Ann. Sc. E.N.S. (to appear).
S. Gelbart and A. Knapp, L-indistinguiskability and R-groups for the special linear group, Adv. in Math. 43 (1982), 101-121.
Harish-Chandra, Harmonic analysis on reductive p-adic groups, Proc. Symp. Pure Math. XXVI (1974), 167–192.
Harish-Chandra, Admissible invariant distributions on reductive p-adic groups, Queen’s Papers in Pure and Applied Math. 48 (1978), 281–347.
Harish-Chandra, A submersion principle and its applications, Proc. Indian Acad. Sci. (Math. Sci.) 90 (1981), 95–102.
Harish-Chandra, The Plancherel formula for reductive p-adic groups, Collected Papers, Vol. IV, Springer-Verlag, Berlin-Heidelberg-New York, 1984.
Harish-Chandra, Letter to M.-F. Vignéras, 1982.
Harish-Chandra, Supertempered distributions on real reductive groups, Stud. App. Math.Adv. Math. 8 (1983), 139–153.
H. Jacquet and R. P. Langlands, Automorphic forms on GL(2), Lecture Notes in Math., Vol 114, Springer-Verlag, Berlin-New York, 1970.
D. Kazhdan, Cuspidal geometry of p-adic groups, J. Analyse Math. 47 (1986), 1–36.
D. Kazhdan, On lifting, Lie groups representations II, Lecture Notes in Math., Vol. 1041 (R. Herb, ed.), Springer-Verlag, Berlin-Heidelberg-New York, 1984.
D. Keys, On the decomposition of reducible principal series representations of p-adic Chevalley groups, Pacific J. Math. 101 (1982), 351–388.
A. Knapp and G. Zuckerman, Classification of irreducible tempered representations of semi-simple groups, Ann. Math. 116 (1982), 389–501.
R. Kottwitz and J. Rogawski, The distributions in the invariant trace formula are supported on characters, preprint.
R. P. Langlands, Les débuts d’une formule des traces stable, Publ. Math. Univ., Paris 7, Paris, undated.
J. Rogawski, Applications of the building to orbital integral, Ph.D. Thesis, Princeton University, Princeton, 1980.
J. Rogawski, Representations of GL(n) and division algebras over a p-adic field, Duke Math. J. 50 (1983), 161–169.
A. Silberger, Introduction to Harmonic Analysis on Reductive p-adic Groups, Princeton Univ. Press, Princeton, New Jersey, 1979.
M.-F. Vignéras, Caractérisation des intégrales orbitales sur un groupe réductif p-adique, J. Fac. Sc. Univ. Tokyo, Sec. IA 29 (1981), 945–962.
M.-F. Vignéras, On formal degrees of projective modules for reductive p-adic groups, preprint.
N. Winarsky, Reducibility of principal series representations of p-adic Chevalley groups, Amer. J. Math. 100 (1978), 941–956.
P.A. Mischenko, Invariant tempered distributions on the reductive p-adic group GL n ( p ), C. R. Math. Acad. Sc, Soc. Roy. du Canada 4 (1982), 123–127.
P.A. Mischenko, Invariant tempered distributions on the reductive group GL n (F p ), Ph.D. Thesis, University of Toronto, Toronto, 1982.
W. Casselman, Characters and Jacquet modules, Math. Ann. 230 (1977), 101–105.
P. Deligne, D. Kazhdan, M.-F. Vignéras, Représentations, des algèbres centrales simples p-adiques, Représentations des Groupes Réductifs sur un Corps Local, Hermann, Paris, 1984, pp. 33-117.
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Clozel, L. (1991). Invariant Harmonic Analysis on the Schwartz Space of a Reductive p-ADIC Group. In: Barker, W.H., Sally, P.J. (eds) Harmonic Analysis on Reductive Groups. Progress in Mathematics, vol 101. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0455-8_6
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