DOCUMENTA MATHEMATICA, Extra Volume ICM II (1998), 553-562

Robert E. Kottwitz

Title: Harmonic Analysis on Semisimple p-Adic Lie Algebras

Certain topics in harmonic analysis on semisimple groups arise naturally when one uses the Arthur-Selberg trace formula to study automorphic representations of adele groups. These topics, which fall under the heading of ``comparison of orbital integrals,'' have been surveyed in Waldspurger's article in the the proceedings of ICM94. As in Harish-Chandra's work, many questions in harmonic analysis on the group can be reduced to analogous questions on its Lie algebra, and in particular this is the case for ``comparison of orbital integrals.'' We will discuss some recent work of this type.

1991 Mathematics Subject Classification: 22E35, 22E50, 11F85

Keywords and Phrases: Orbital integrals, $p$-adic, Lie algebra

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