When Harish-Chandra died in 1983, he left behind a voluminous pile of handwritten manuscripts on harmonic analysis on semisimple Lie groups over real/complex and p-adic fields. The manuscripts were turned over to the archives of the Institute for Advanced Study at Princeton, and are archived there.
Robert Langlands is the Trustee of the Harish-Chandra archive, and has always been interested in finding a way of salvaging whatever might be valuable in these manuscripts. Some years ago, at a conference in UCLA, he encouraged V. S. Varadarajan and me to look at these manuscripts.
The results of our efforts have resulted in the publication of the Volume 5 (Posthumous) of the Collected works of Harish-Chandra by Springer Verlag, which appeared in July this year. This volume covers only those manuscripts that deal with Real or Complex groups. The manuscripts dealing with p-adic groups remain in the archive.
My talk will be devoted to an outline of the results in this volume, without much detail. However, I will try to describe the main ingredient of the methods that cut across most of this work.