By Neil Chriss, Victor Ginzburg

This vintage monograph offers an summary of contemporary advances in illustration concept from a geometrical viewpoint. A geometrically-oriented remedy of the topic is particularly well timed and has lengthy been wanted, in particular because the discovery of D-modules within the early Nineteen Eighties and the quiver method of quantum teams within the early Nineteen Nineties. The options built are fairly basic and will be effectively utilized to different parts corresponding to quantum teams, affine Lie teams, and quantum box conception. the 1st half the publication fills the space among the traditional wisdom of a newbie in Lie concept and the a lot wider heritage wanted by way of the operating mathematician.

*The ebook is basically self-contained. . . . there's a great advent to symplectic geometry and a captivating exposition of equivariant K-theory. either are enlivened by means of examples on the topic of teams. . . . an enticing function is the try and show a few casual 'wisdom' instead of in basic terms the correct definitions. As a few effects is because of the authors, one reveals a number of the unique pleasure. this is often the single to be had creation to geometric illustration thought. . . it has already proved winning in introducing a brand new iteration to the subject.*

*--- Bulletin of the yankee Mathematical Society*

*The authors have attempted to assist readers through adopting a casual and simply obtainable type. . . . The e-book will offer a consultant to people who desire to penetrate into subject-matter which, thus far, was once merely obtainable in tricky papers. . . . The ebook is sort of appropriate as a foundation for a complicated direction or a seminar, dedicated to the cloth of 1 of the chapters of the book.*

*--- Mededelingen van het Wiskundig Genootschap*

*Represents a massive and intensely attention-grabbing addition to the literature.*

*--- Mathematical Reviews*