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Reflection Groups and Coxeter Groups

Reflection Groups and Coxeter Groups

$53.95 (P)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: October 1992
  • availability: Available
  • format: Paperback
  • isbn: 9780521436137

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About the Authors
  • 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.

    • Jim Humphreys is one of the best-known names in group theory
    • The paperback has been updated and corrected
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    Reviews & endorsements

    "This is a book which can be recommended to both beginners and more experienced workers with an interest in Coxeter groups. In common with all of Humphrey's books, it is written in a clear and helpful expository style, and so gives an excellent introduction to the subject. At the same time the material dealing with recent developments such as Kazhdan-Lusztig theory will be most useful to specialists in the area." Bulletin of the London Mathematical Society

    "...a useful book. The style is informal and the arguments are clear." Louis Solomon, Mathematical Reviews

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    Product details

    • Date Published: October 1992
    • format: Paperback
    • isbn: 9780521436137
    • length: 220 pages
    • dimensions: 229 x 156 x 15 mm
    • weight: 0.35kg
    • availability: Available
  • Table of Contents

    Part I. Finite and Affine Reflection Groups:
    1. Finite reflection groups
    2. Classification of finite reflection groups
    3. Polynomial invariants of finite reflection groups
    4. Affine reflection groups
    Part II. General Theory of Coxeter Groups:
    5. Coxeter groups
    6. Special case
    7. Hecke algebras and Kazhdan–Lusztig polynomials
    8. Complements
    Bibliography.

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    Reflection Groups and Coxeter Groups

    James E. Humphreys

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  • Author

    James E. Humphreys, University of Massachusetts, Amherst
    James E. Humphreys was born in Erie, Pennsylvania, and received his A.B. from Oberlin College, 1961, and his Ph.D. from Yale University, 1966. He has taught at the University of Oregon, Courant Institute (NYU), and the University of Massachusetts at Amherst (now retired). He visits IAS Princeton, Rutgers. He is the author of several graduate texts and monographs.

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