Ebook: Kac-Moody Groups, their Flag Varieties and Representation Theory
Author: Shrawan Kumar (auth.)
- Tags: Topological Groups Lie Groups, Algebra, Algebraic Geometry, Group Theory and Generalizations
- Series: Progress in Mathematics 204
- Year: 2002
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.
Content:
Front Matter....Pages i-xv
Kac-Moody Algebras....Pages 1-37
Representation Theory of Kac-Moody Algebras....Pages 39-65
Lie Algebra Homology and Cohomology....Pages 67-107
An Introduction to ind-Varieties and pro-Groups....Pages 109-148
Tits Systems....Pages 149-171
Kac-Moody Groups....Pages 173-197
Generalized Flag Varieties of Kac-Moody Groups....Pages 199-244
Demazure and Weyl-Kac Character Formulas....Pages 245-294
BGG and Kempf Resolutions....Pages 295-336
Defining Equations of G/P and Conjugacy Theorems....Pages 337-368
Topology of Kac-Moody Groups and Their Flag Varieties....Pages 369-445
Smoothness and Rational Smoothness of Schubert Varieties....Pages 447-479
An Introduction to Affine Kac Moody Lie Algebras and Groups....Pages 481-510
Back Matter....Pages 511-609
Content:
Front Matter....Pages i-xv
Kac-Moody Algebras....Pages 1-37
Representation Theory of Kac-Moody Algebras....Pages 39-65
Lie Algebra Homology and Cohomology....Pages 67-107
An Introduction to ind-Varieties and pro-Groups....Pages 109-148
Tits Systems....Pages 149-171
Kac-Moody Groups....Pages 173-197
Generalized Flag Varieties of Kac-Moody Groups....Pages 199-244
Demazure and Weyl-Kac Character Formulas....Pages 245-294
BGG and Kempf Resolutions....Pages 295-336
Defining Equations of G/P and Conjugacy Theorems....Pages 337-368
Topology of Kac-Moody Groups and Their Flag Varieties....Pages 369-445
Smoothness and Rational Smoothness of Schubert Varieties....Pages 447-479
An Introduction to Affine Kac Moody Lie Algebras and Groups....Pages 481-510
Back Matter....Pages 511-609
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