Kac-Moody groups, their flag varieties, and representation theory /

• Main Author: Kumar, Shrawan, 1953-
• Format: Book
• Language: English
• Published: Boston : Birkhaüaser, c2002.
• Series: Progress in mathematics ; v. 204
• Subjects: Grupos de Lie.; Algebras no asociativas.; Anillos no asociativos.; Algebras de Kac-Moody.; Lie groups.; Nonassociative algebras.; Nonassociative rings.; Kac-Moody algebras.; Representations of groups.; Flag manifolds.

Table of Contents:

• I. Kac-Moody Algebras: Basic Theory
• II. Representation Theory of Kac-Moody Algebras
• III. Lie Algebra Homology and Cohomology
• IV. An Introduction to ind-Varieties and pro-Groups
• V. Tits Systems: Basic Theory
• VI. Kac-Moody Groups: Basic Theory
• VII. Generalized Flag Varieties of Kac-Moody Groups
• VIII. Demazure and Weyl-Kac Character Formulas
• IX. BGG and Kempf Resolutions
• X. Defining Equations of G/P and Conjugacy Theorems
• XI. Topology of Kac-Moody Groups and Their Flag Varieties
• XII. Smoothness and Rational Smoothness of Schubert Varieties
• XIII. An Introduction to Affine Kac-Moody Lie Algebras and Groups
• App. A. Results from Algebraic Geometry
• App. B. Local Cohomology
• App. C. Results from Topology
• App. D. Relative Homological Algebra
• App. E. An Introduction to Spectral Sequences.