Harish-Chandra was a mathematician of great power, vision, and remarkable ingenuity. His profound contributions to the representation theory of Lie groups, harmonic analysis, and related areas left researchers a rich legacy that continues today. This book presents the proceedings of an AMS Special Session entitled, "Representation Theory and Noncommutative Harmonic Analysis: A Special Session Honoring the Memory of Harish-Chandra", which marked 75 years since his birth and 15 years since his untimely death at age 60.

Contributions to the volume were written by an outstanding group of internationally known mathematicians. Included are expository and historical surveys and original research papers. The book also includes talks given at the IAS Memorial Service in 1983 by colleagues who knew Harish-Chandra well. Also reprinted are two articles entitled, "Some Recollections of Harish-Chandra", by A. Borel, and "Harish-Chandra's c-Function: A Mathematical Jewel", by S. Helgason. In addition, an expository paper, "An Elementary Introduction to Harish-Chandra's Work", gives an overview of some of his most basic mathematical ideas with references for further study.

This volume offers a comprehensive retrospective of Harish-Chandra's professional life and work. Personal recollections give the book particular significance. Readers should have an advanced-level background in the representation theory of Lie groups and harmonic analysis.

For other wonderful titles written by this author see: Euler through Time: A New Look at Old Themes, Supersymmetry for Mathematicians: An Introduction, The Selected Works of V.S. Varadarajan, and Algebra in Ancient and Modern Times.

Readership

Graduate students and research mathematicians interested in representation theory of Lie groups and harmonic analysis; historians of mathematics.

Table of Contents

• V. S. Varadarajan -- Harish-Chandra, his work, and its legacy
• A. Borel -- Some recollections of Harish-Chandra
• S. Helgason -- Harish-Chandra memorial talk
• R. P. Langlands -- Harish-Chandra memorial talk
• G. D. Mostow -- Harish-Chandra memorial talk
• V. S. Varadarajan -- Harish-Chandra memorial talk
• R. A. Herb -- An elementary introduction to Harish-Chandra's work
• J. Arthur -- Stabilization of a family of differential equations
• D. Barbasch -- Orbital integrals of nilpotent orbits
• P. F. Baum, N. Higson, and R. J. Plymen -- Representation theory of $p$-adic groups: A view from operator algebras
• W. Casselman, H. Hecht, and D. Miličić -- Bruhat filtrations and Whittaker vectors for real groups
• S. DeBacker and P. J. Sally, Jr. -- Germs, characters, and the Fourier transforms of nilpotent orbits
• H. Ding, K. I. Gross, R. A. Kunze, and D. St. P. Richards -- Bessel functions on boundary orbits and singular holomorphic representations
• B. Gross and N. Wallach -- Restriction of small discrete series representations to symmetric subgroups
• S. Helgason -- Harish-Chandra's c-function. A mathematical jewel
• R. A. Herb -- Two-structures and discrete series character formulas
• R. E. Howe -- Harish-Chandra homomorphisms
• P. E. T. Jorgensen and G. Ólafsson -- Unitary representations and Osterwalder-Schrader duality
• A. W. Knapp -- Intertwining operators and small unitary representations
• R. A. Kunze -- On some problems in analysis suggested by representation theory
• R. L. Lipsman -- Distributional reciprocity and generalized Gelfand pairs
• A. Moy -- Displacement functions on the Bruhat-Tits building
• F. Murnaghan -- Germs of characters of admissible representations
• B. Speh -- Seiberg-Witten equations on locally symmetric spaces
• J. A. Wolf and R. Zierau -- Holomorphic double fibration transforms