Reflection Groups and Coxeter Groups

ISBN-10: 0521436133
ISBN-13: 9780521436137
Edition: N/A
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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  More...

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Book details

Publisher: Cambridge University Press
Publication date: 10/1/1992
Binding: Paperback
Pages: 220
Size: 6.00" wide x 9.25" long x 0.50" tall
Weight: 0.990
Language: English

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.

Finite and Affine Reflection Groups
Finite reflection groups
Classification of finite reflection groups
Polynomial invariants of finite reflection groups
Affine reflection groups
General Theory of Coxeter Groups
Coxeter groups
Special case
Hecke algebras and Kazhdan-Lusztig polynomials
Complements
Bibliography

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