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Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics)

Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics)

Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics)
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Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics) Paperback - 1992

by J. E. Humphreys, B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak

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  • Title Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics)
  • Author J. E. Humphreys, B. Bollobas, W. Fulton, A. Katok, F. Kirwan, P. Sarnak
  • Binding Paperback
  • Edition Reprint
  • Condition New
  • Pages 220
  • Volumes 1
  • Language ENG
  • Publisher Cambridge University Press, Cambridge
  • Publication date 1992-10-01
  • Illustrated Yes
  • Features Illustrated, Index, Table of Contents
  • Bookseller's Inventory # 696949-n
  • ISBN 9780521436137 / 0521436133
  • Weight 0.77 lbs (0.35 kg)
  • Dimensions 9.02 x 6.16 x 0.6 in (22.91 x 15.65 x 1.52 cm)
  • Category Mathematics
  • Library of Congress subjects Coxeter groups, Reflection groups
  • Library of Congress Catalogue Number 93109267
  • Dewey Decimal Code 512.2
  • Quantity available 5

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From the publisher

In this graduate textbook Professor Humphreys presents a concrete and up-to-date introduction to the theory of Coxeter groups. He assumes that the reader has a good knowledge of algebra, but otherwise the book is self contained. The first part is devoted to establishing concrete examples; the author begins by developing the most important facts about finite reflection groups and related geometry, and showing that such groups have a Coxeter representation. In the next chapter these groups are classified by Coxeter diagrams, and actual realizations of these groups are discussed. Chapter 3 discusses the polynomial invariants of finite reflection groups, and the first part ends with a description of the affine Weyl groups and the way they arise in Lie theory. The second part (which is logically independent of, but motivated by, the first) starts by developing the properties of the Coxeter groups. Chapter 6 shows how earlier examples and others fit into the general classification of Coxeter diagrams. Chapter 7 is based on the very important work of Kazhdan and Lusztig and the last chapter presents a number of miscellaneous topics of a combinatorial nature.

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