reflection groups and coxeter groups

Reflection Groups and Coxeter Groups (Cambridge Studies in Advanced Mathematics)
AuthorJames E. Humphreys

Publisher: Cambridge University Press

Edition: ed

Print length: 220

Publication date: 1992-10-30

ISBN-10: 0521436133

ISBN-13: 9780521436137
Product
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 Authordeveloping 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 AuthorCoxeter 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 Authordeveloping 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.