Collected Papers V (Posthumous): Harmonic Analysis in Real Semisimple Groups

This volume is to be regarded as the fifth in the series of Harish-Chandra’s collected papers, continuing the four volumes already published by Springer-Verlag. Because of manifold illnesses in the last ten years of his life, a large part of Harish-Chandra’s work remained unpublished. The present volume deals with those unpublished manuscripts involving real groups, and includes only those pertaining to the theorems which Harish-Chandra had announced without proofs.

An attempt has been made by the volume editors to bring out this material in a more coherent form than in the handwritten manuscripts, although nothing essentially new has been added and editorial comments are kept to a minimum. The papers deal with several topics: characters on non-connected real groups, Fourier transforms of orbital integrals, Whittaker theory, and supertempered characters. The generality of Harish-Chandra’s results in these papers far exceeds anything in print.

The volume will be of great interest to all mathematicians interested in Lie groups, and all who have an interest in the opus of a twentieth century giant. Harish-Chandra was a great mathematician, perhaps one of the greatest of the second half of the twentieth century.

V.S. Varadarajan is a mathematician of Indian origin. He was born in Chennai, India in 1937 and did his graduate work under Dr. C.R. Rao, in the years 1956–1960, when Dr. Rao was the research director of the Indian Statistical Institute, Calcutta. He and his coworkers at that time, K.R. Parthasarathy, R. Ranga Rao, and S.R.S. Varadhan, are generally credited with the creation of an Indian school of probability. After short periods at the Institute for Advanced Study and the University of Washington, Seattle, he joined the Department of Mathematics at UCLA in 1965. He was awarded the Onsager Medal in 1998. He has worked for a number of years in the representation theory of semi-simple groups, which is also a topic that consumed Harish-Chandra, and he has also made contributions to ordinary differential equations with a fixed irregular singularity. Recently, he has been interested in p-adic analysis as well as mathematics inspired by issues of supersymmetry in the physics of elementary particles. He is deeply interested in the development of Indian mathematics, and in South Indian and Western classical music.He is currently Professor Emeritus and Distinguished Research Professor of Mathematics  at the University of California at Los Angeles. 

Ramesh Gangolli was born in Bangalore, India, and educated at the Universities of Bombay and Cambridge, and at MIT.  After taking his doctoral degree at MIT, he taught there for a year before joining the faculty of the University of Washington, Seattle, in 1962.  Since then, he has been a faculty member in the Department of Mathematics, serving as Chair in the years 1981–85 and 1991–93.  He has been active in mathematical research as well as in education during his career. He was a Sloan Foundation Fellow (1966–68) and a Member of the Institute for Advanced Study, Princeton (1966–67). In 1966 he was awarded the Prix Paul Lévy by the Academy of Sciences of France.  Ramesh Gangolli also maintains a serious interest in the classical music of North India and teaches in the Ethnomusicology Program in the School of Music. He is currently Professor Emeritus of Mathematics and Adjunct Professor of Music at the University of Washington. In 1981 he helped to found Ragamala – a volunteer organization based in Seattle, devoted to the Music of India and South Asia.