Reflection Groups and Coxeter Group

Erscheinungsjahr 1992
ISBN: 978-0-521-43613-7
Verlag: Cambridge University Press

Buch, Englisch, Band 29, 216 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 365 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Humphreys, James E.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

Humphreys, James E.
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.