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.
A self-contained graduate textbook introducing the basic theory of Coxeter groups.
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.
"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
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