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.
A self-contained graduate textbook introducing the basic theory of Coxeter groups.
About the Author
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.
Reviews
"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
Book Information
ISBN 9780521436137
Author James E. Humphreys
Format Paperback
Page Count 220
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 350g
Dimensions(mm) 229mm * 156mm * 15mm
A self-contained graduate textbook introducing the basic theory of Coxeter groups.
About the Author
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.
Reviews
"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
Book Information
ISBN 9780521436137
Author James E. Humphreys
Format Paperback
Page Count 220
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 350g
Dimensions(mm) 229mm * 156mm * 15mm
