| Kac-Moody Groups, Their Flag Varieties and Representation Theory 2002 Edition Contributor(s): Kumar, Shrawan (Author) |
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ISBN: 0817642277 ISBN-13: 9780817642273 Publisher: Birkhauser OUR PRICE: $123.49 Product Type: Hardcover - Other Formats Published: September 2002 Annotation: This is the first monograph to exclusively treat Kac-Moody (K-M) groups, a standard tool in mathematics and mathematical physics. K-M Lie algebras were introduced in the mid-sixties independently by V. Kac and R. Moody, generalizing finite-dimensional semisimple Lie algebras. K-M theory has since undergone tremendous developments in various directions and has profound connections with a number of diverse areas, including number theory, combinatorics, topology, singularities, quantum groups, completely integrable systems, and mathematical physics. This comprehensive, well-written text moves from K-M Lie algebras to the broader K-M Lie group setting, and focuses on the study of K-M groups and their flag varieties. In developing K-M theory from scratch, the author systematically leads readers to the forefront of the subject, treating the algebro-geometric, topological, and representation-theoretic aspects of the theory. Most of the material presented here is not available anywhere in the book literature. {\it Kac--Moody Groups, their Flag Varieties and Representation Theory} is suitable for an advanced graduate course in representation theory, and contains a number of examples, exercises, challenging open problems, comprehensive bibliography, and index. Research mathematicians at the crossroads of representation theory, geometry, and topology will learn a great deal from this text; although the book is devoted to the general K-M case, those primarily interested in the finite-dimensional case will also benefit. No prior knowledge of K-M Lie algebras or of (finite-dimensional) algebraic groups is required, but some basic knowledge would certainly be helpful. For the reader's convenience someof the basic results needed from other areas, including ind-varieties, pro-algebraic groups and pro-Lie algebras, Tits systems, local cohomology, equivariant cohomology, and homological algebra are included. |
| Additional Information |
| BISAC Categories: - Mathematics | Group Theory - Science | Physics - Mathematical & Computational - Mathematics | Algebra - Linear |
| Dewey: 512.55 |
| LCCN: 2002018302 |
| Series: Progress in Mathematics |
| Physical Information: 1.26" H x 6.24" W x 9.42" (2.34 lbs) 609 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |