Reflection Groups and Coxeter Groups - James E. Humphreys Reflection Groups and Coxeter Groups - James E. Humphreys - Google Books In this graduate textbook Professor Humphreys presents a concrete and up-to-date introduction to the theory of Coxeter.. Reflection Groups and Coxeter Groups by James E. Humphreys 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. Reflection Groups and Coxeter Groups PDF James E. Humphreys Reflection Groups and Coxeter Groups PDF James E. Humphreys 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. Reflection group - Wikipedia In group theory and geometry, a reflection group is a discrete group which is generated by a set of reflections of a finite-dimensional Euclidean space symmetry group of a regular polytope or of a tiling of the Euclidean space by congruent copies of a regular polytope is necessarily a reflection group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. Coxeter group - Wikipedia The abstract group of a reflection group is a Coxeter group, while conversely a reflection group can be seen as a linear representation of a Coxeter group. For finite reflection groups, this yields an exact correspondence: every finite Coxeter group admits a faithful representation as a finite reflection group of some Euclidean space. For infinite Coxeter groups, however, a Coxeter group may not admit a representation as a reflection group.
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