Representation Theory and Complex Geometry

by Neil Chriss

"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)

Genres: Mathematics

505 pages, Hardcover

First published February 18, 1997

Reviews

[Andrew · Rating 4 out of 5]

I love the book's aesthetic preference for geometry. See for example the approach to the Bruhat decomposition via Bialinicki-Birula (where you can imagine a really nice picture) rather than the computational BN pairs. The book's treatment of its subjects fall along this line: instead of the combinatorial approach to the representation theory of the symmetric group, we use Springer's geometric constructions of these representations which gives geometric meaning to the underlying finite group representation theory. Routinely, CG eschew generality to make the picture more concrete, or add explanatory comments before getting to the formal details of the proof. These are really helpful for learning.