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Kac-Moody Groups, Their Flag Varieties and Representation Theory
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Home > Mathematics Books > Group Theory > Item 115
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Kac-Moody Groups, Their Flag Varieties and Representation Theory
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by Shrawan Kumar and S. Kumar
Sales Rank: 1570089
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List Price: $79.95
$64.09
At Amazon
on 12-6-2008
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Hardcover: 632 pages
Publisher: Birkhäuser Boston; 1 edition September 10, 2002
Language: English
ISBN-10: 0817642277
ISBN-13: 978-0817642273
Product Dimensions:
9.3 x 6.2 x 1.3 inches
Shipping Weight: 2.3 pounds
Product Review
"Most of these topics appear here for the first time in book form. Many of them are interesting even in the classical case of semi-simple algebraic groups. Some appendices recall useful results from other areas, so the work may be considered self-contained, although some familiarity with semi-simple Lie algebras or algebraic groups is helpful. It is clear that this book is a valuable reference for all those interested in flag varieties and representation theory in the semi-simple or Kac-Moody case."
—MATHEMATICAL REVIEWS
"A lot of different topics are treated in this monumental work. . . . many of the topics of the book will be useful for those only interested in the finite-dimensional case. The book is self contained, but is on the level of advanced graduate students. . . . For the motivated reader who is willing to spend considerable time on the material, the book can be a gold mine. "
—ZENTRALBLATT MATH
Product Description
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 some of 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.
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Kac-Moody Groups, Their Flag Varieties and Representation Theory
Available from Amazon
Price: $64.09
Updated on 12-6-2008
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