Representation Theory and Complex Geometry [Paperback]

The book is largely self-contained...There is a nice introduction to symplectic geometry and a charming exposition of equivariant K-theory. 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 [are] 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)

This volume provides an overview of modern advances in representation theory from a geometric standpoint. The techniques developed are quite general and can be applied to other areas such as quantum groups, affine Lie groups, and quantum field theory.

Preface.- Chapter 0. Introduction.- Chapter 1. Symplectic Geometry.- Chapter 2. Mosaic.- Chapter 3. Complex Semisimple Groups.- Chapter 4. Springer Theory.- Chapter 5. Equivariant K-Theory.- Chapter 6. Flag Varieties, K-Theory, and Harmonic Polynomials.- Chapter 7. Hecke Algebras and K-Theory.- Chapter 8. Representations of Convolution Algebras.- Bibliography.

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 self-contained.... There is a nice introduction to symplectic geometry and a charming exposilSx