Representation Theory of Reductive Groups : Proceedings of the University of Utah Conference 1982 This volume is the result of a conference on Representation Theory of Reductive Groups held in Park City Utah April 16 20 1982 under the auspices of the Department of Mathematics University of Utah. Funding for the conference was provided by the National Science Foundation. The text includes a number of original papers together with expository articles on work already in print. It is hoped that the volume will be of use to both experts in the field and nonspecialists interested in obtaining some insight into the area. Principal organizers of the conference were Henryk Hecht Dragan Mili~ie and Peter Trombi. They would like to express their thanks to the National Science Foundation for their support to the speakers for their diligence in submitting their manuscripts and to Carla Curtis Karen Edge and Katherine Ruth for typing the manuscripts which were contributed. v CONTENTS J. Arthur Multipliers and a Paley Wiener theorem for real reductive groups .......................................... . Multipliers and a Paley Wiener theorem for real reductive groups Weyl group representations and nilpotent orbits A generalization of Casselman’ s submodule theorem Fourier transforms of orbits of the coadjoint representation IL2 cohomology for groups of real rank one Character relations between singular holomorphic representations A classification of unitary highest weight modules The range of the Radon transform on a symmetric space Weighted orbital integrals Reciprocity laws in the theory of dual pairs Characters of the discrete series for pseudo Riemannian symmetric spaces All supercuspidal representations of SL over a p adic field are induced A note on invariant forms on locally symmetric spaces Oscillatory integrals and their application to harmonic analysis on semisimple Lie groups The Kazhdan Lusztig conjecture for real reductive groups Completeness of Poincaré series for automorphic forms associated to the integrable discrete series Geometric methods in representation theory.