Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics, Series Number 29)
ISBN-13:
9780521375108
ISBN-10:
052137510X
Edition:
Pbk (W/Corrections) ed.
Author:
James E. Humphreys
Publication date:
1990
Publisher:
Cambridge University Press
Format:
Hardcover
213 pages
Category:
Pure Mathematics
,
Mathematics
FREE US shipping
Book details
ISBN-13:
9780521375108
ISBN-10:
052137510X
Edition:
Pbk (W/Corrections) ed.
Author:
James E. Humphreys
Publication date:
1990
Publisher:
Cambridge University Press
Format:
Hardcover
213 pages
Category:
Pure Mathematics
,
Mathematics
Summary
Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics, Series Number 29) (ISBN-13: 9780521375108 and ISBN-10: 052137510X), written by authors
James E. Humphreys, was published by Cambridge University Press in 1990.
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Description
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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