Download Reflection Groups and Coxeter Groups (Cambridge Studies in by James E. Humphreys PDF

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By James E. Humphreys

This graduate textbook provides a concrete and up to date advent to the speculation of Coxeter teams. The booklet is self-contained, making it appropriate both for classes and seminars or for self-study. the 1st half is dedicated to setting up concrete examples. Finite mirrored image teams performing on Euclidean areas are mentioned, and the 1st half ends with the development of the affine Weyl teams, a category of Coxeter teams that performs a massive position in Lie idea. the second one half (which is logically autonomous of, yet encouraged by means of, the 1st) develops from scratch the homes of Coxeter teams quite often, together with the Bruhat ordering and the seminal paintings of Kazhdan and Lusztig on representations of Hecke algebras linked to Coxeter teams is brought. ultimately a couple of fascinating complementary themes in addition to connections with Lie thought are sketched. The ebook concludes with an in depth bibliography on Coxeter teams and their applications.

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