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Representation theory and complex geometry. (English) Zbl 0879.22001
Boston, MA: Birkhäuser. x, 495 p. (1997).
This book treats the study of the geometry associated with a complex semisimple Lie group, such as the geometry of flag varieties, nilpotent conjugacy classes, Springer resolutions etc. For this study, the main tools used are symplectic geometry, equivariant algebraic $$K$$-theory and convolution operation in homology. The book also presents a uniform geometric approach to the classification of finite-dimensional irreducible representations of Weyl groups, the Lie algebra $${\mathfrak sl} (\mathbb{C})$$ and affine Hecke algebras. This book is a nice blend of Algebraic Geometry, Symplectic Geometry and Representation Theory.

##### MSC:
 22-02 Research exposition (monographs, survey articles) pertaining to topological groups 17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry