Representation Theory and Complex Geometry
Authors: Chriss, Neil, Ginzburg, Victor
Free PreviewBuy this book
 About this book

This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometricallyoriented treatment of the subject is very timely and has long been desired, especially since the discovery of Dmodules in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Lie groups, and quantum field theory. The first half of the book fills the gap between the standard knowledge of a beginner in Lie theory and the much wider background needed by the working mathematician.
The book is largely selfcontained. . . . There is a nice introduction to symplectic geometry and a charming exposition of equivariant Ktheory. Both are enlivened by examples related to groups. . . . An attractive feature is the attempt to convey some informal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory. . . it has already proved successful in introducing a new generation to the subject.
 Bulletin of the American Mathematical Society
The authors have tried to help readers by adopting an informal and easily accessible style. . . . The book will provide a guide to those who wish to penetrate into subjectmatter which, so far, was only accessible in difficult papers. . . . The book is quite suitable as a basis for an advanced course or a seminar, devoted to the material of one of the chapters of the book.
 Mededelingen van het Wiskundig Genootschap
Represents an important and very interesting addition to the literature.
 Mathematical Reviews
 Reviews

From the reviews:
"The authors have tried to help readers by adopting an informal and easily accessible style...to convey a sound intuitive grasp of the basic concepts and proofs... The book will provide a guide to those who wish to penetrate into subject matter which, so far, was only accessible in difficult papers... The book is quite suitable as a basis for an advanced course or a seminar." T.A. Springer (Mededelingen van het wiskundig genootschap)
"Represents an important and very interesting addition to the literature."  Mathematical Reviews
"The book is largely selfcontained.... There is a nice introduction to symplectic geometry and a charming exposition of equivariant Ktheory. Both are enlivened by examples related to groups... An attractive feature is the attempt to convey some informal 'wisdom' rather than only the precise definitions. As a number of results is due to the authors, one finds some of the original excitement. This is the only available introduction to geometric representation theory...it has already proved successful in introducing a new generation to the subject."  Bulletin of the AMS
“The material covered in this book is at the crossroads of algebraic geometry, symplectic geometry and ‘pure’ representation theory. … This volume provides a selfcontained overview of some of the recent advances in representation theory from a geometric standpoint. … The techniques developed are quite general and can be successfully applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.” (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1185, 2010)
 Table of contents (9 chapters)


Introduction
Pages 119

Symplectic Geometry
Pages 2159

Mosaic
Pages 61126

Complex Semisimple Groups
Pages 127192

Springer Theory for u (sln)
Pages 193230

Table of contents (9 chapters)
Recommended for you
Bibliographic Information
 Bibliographic Information

 Book Title
 Representation Theory and Complex Geometry
 Authors

 Neil Chriss
 Victor Ginzburg
 Copyright
 2010
 Publisher
 Birkhäuser Basel
 Copyright Holder
 Birkhäuser Boston
 eBook ISBN
 9780817649388
 DOI
 10.1007/9780817649388
 Hardcover ISBN
 9780817637927
 Softcover ISBN
 9780817649371
 Edition Number
 1
 Number of Pages
 X, 495
 Number of Illustrations
 5 b/w illustrations
 Topics