Paul Sally

David A. Vogan

This book brings together five papers that have been influential in the study of Lie groups. Though published more than 20 years ago, these papers made fundamental contributions that deserve much broader exposure. In addition, the subsequent literature that has subsumed these papers cannot replace the originality and vitality they contain. The editors have provided a brief introduction to each paper, as well as a synopsis of the major developments which have occurred in the area covered by each paper. Included here are the doctoral theses of Arthur, Osborne, and Schmid. Arthur's thesis is closely related to Trombi's paper insofar as both deal with harmonic analysis on real semisimple Lie groups, and, in particular, analysis on the Schwartz space of Harish-Chandra. Arthur's thesis is concerned with the image under the Fourier transform of the Schwartz space of a semisimple Lie group of real rank one, while Trombi's paper provides an expository account of the harmonic analysis associated to the decomposition of the Schwartz space under the regular representation. In his thesis, Osborne extends the Atiyah-Bott fixed point theorem for elliptic complexes to obtain a fixed point formula for complexes that are not elliptic. Schmid proves a generalization of the Borel-Weil theorem concerning an explicit and geometric realization of the irreducible representations of a compact, connected semisimple Lie group. Langlands's fundamental paper provides a classification of irreducible, admissible representations of real reductive Lie groups.

Representation Theory and Harmonic Analysis on Semisimple Lie Groups

Judith Sally

Swim, Run, and Bike your way to math success! Judith and Paul Sally, accomplished mathematicians and experienced teachers, offer a challenging athletic workout to the minds of their young readers through exercises in areas of number theory and geometry that extend beyond the realm of basic mathematics in the school curriculum. The activities in the book present readers with a dynamic and fresh perspective on mathematics, encouraging active and energetic responses leading to a level of thinking that carries over into college mathematics. The book's novel games coach the players to experience the satisfaction and confidence that accompany meaningful investigations of mathematical ideas. This book will provide a stimulus to make scientific competition as much a part of our educational culture as the athletic activities to which we are accustomed.

Paul Sally

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