Representation Theory of Lie Groups
About this Title
Jeffrey Adams, University of Maryland, College Park, College Park, MD and David Vogan, Massachusetts Institute of Technology, Cambridge, MA, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 2000; Volume 8
ISBNs: 978-1-4704-2314-8 (print); 978-1-4704-3907-1 (online)
MathSciNet review: MR1743154
MSC: Primary 22-06
This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification.
Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant “philosophy of coadjoint orbits” for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of “localization”. And Jian-Shu Li covers Howe's theory of “dual reductive pairs”.
Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory.
Graduate students and research mathematicians interested in representation theory specifically Lie groups and their representations.
Table of Contents
- Representations of semisimple Lie groups
- Representations in Dolbeault cohomology
- Unitary representations attached to elliptic orbits. A geometric approach
- The method of adjoint orbits for real reductive groups
- Geometric methods in representation theory
- Minimal representations and reductive dual pairs