Reflection Groups and Coxeter Groups
Published on 29. June 1990
978-1-316-04329-5 (ISBN)
Description
This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications.
Reviews / Votes
"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 ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
File size
11,35 MB
ISBN-13
978-1-316-04329-5 (9781316043295)
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Schweitzer Classification
Other editions
Additional editions
James E. Humphreys
Reflection Groups and Coxeter Groups
Book
10/1992
Cambridge University Press
€70.40
Shipment within 15-20 days
Person
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.
Content
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.
