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  • Textbook
  • © 2002

Kac-Moody Groups, their Flag Varieties and Representation Theory

Birkhäuser

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Part of the book series: Progress in Mathematics (PM, volume 204)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xv
  2. Kac-Moody Algebras

    • Kac-Moody Algebras
    Pages 1-37
  3. Lie Algebra Homology and Cohomology

    • Shrawan Kumar
    Pages 67-107
  4. Tits Systems

    • Shrawan Kumar
    Pages 149-171
  5. Kac-Moody Groups

    • Basic Theory
    Pages 173-197
  6. Demazure and Weyl-Kac Character Formulas

    • Shrawan Kumar
    Pages 245-294
  7. BGG and Kempf Resolutions

    • Shrawan Kumar
    Pages 295-336
  8. Back Matter

    Pages 511-609

About this book

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.

Reviews

"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

Authors and Affiliations

  • Department of Mathematics, University of North Carolina, Chapel Hill, Chapel Hill, USA

    Shrawan Kumar

Bibliographic Information

Buy it now

Buying options

eBook USD 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access