Some Problems in Local Harmonic Analysis
- 575 Downloads
The purpose of this article is to discuss some questions in the harmonic analysis of real and p-adic groups. We shall be particularly concerned with the properties of a certain family of invariant distributions. These distributions arose naturally in a global context, as the terms on the geometric side of the trace formula. However, they are purely local objects, which include the ordinary invariant orbital integrals. One of our aims is to describe how the distributions also arise in a local context. They appear as the terms on the geometric side of a new trace formula, which is simpler than the original one, and is the solution of a natural question in local harmonic analysis. The local trace formula seems to be a promising tool. It might have implications for the difficult local problems which are holding up progress in automorphic forms.
KeywordsParabolic Subgroup Trace Formula Automorphic Form Invariant Distribution Levi Subgroup
Unable to display preview. Download preview PDF.
- 8.J. Arthur, Unipotent automorphic representations: Conjectures, Astérisque 171-172 (1989), 13–71.Google Scholar
- 9.J. Arthur, Towards a local trace formula, Amer. J. Math, (to appear).Google Scholar
- 10.J. Arthur, A local trace formula, preprint.Google Scholar
- 14.L. Clozel and P. Delorme, Le théoreme de Paley-Wiener invariant pour les groupes de Lie réductifs II, Ann. Scient. Ec. Norm. Sup. (to appear).Google Scholar
- 16.Harish-Chandra, The Plancherel formula for reductive p-adic groups, reproduced in Collected Works, Springer-Verlag, Vol. IV, pp. 353-367.Google Scholar
- 19.R. Kottwitz and J. Rogawski, The distributions in the invariant trace formula are supported on characters, preprint.Google Scholar
- 20.R. Langlands, Base Change for GL(2), Annals of Math. Studies 96 (1980), Princeton University Press, Princeton.Google Scholar
- 22.P. Mischenko, Invariant Tempered Distributions on the Reductive p-Adic Group GL n (F p ), Ph.D. Thesis, University of Toronto, Toronto, 1982.Google Scholar