Reflection Groups and Coxeter Group

ISBN-13: 9780521436137 / Angielski / Miękka / 1992 / 220 str.

James E. Humphreys

Opis

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.

Recenzje

"...a useful book. The style is informal and the arguments are clear." Louis Solomon, Mathematical Reviews

Spis treści

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.