Introduction to Coxeter groups


Robert B. Howlett


Research Report 97-6
Lectures delivered at the A.N.U. Geometric Group Theory Workshop
Date: February 1996


These five lectures are an introduction to the theory of Coxeter groups and their geometric realizations as groups of transformations of real vector spaces. In particular the concepts of root basis and the associated root system are described, and used to prove that the geometrical construction yields a faithful representation of a group defined abstractly by a certain presentation. Various properties of the Tits cone are also described, and a proof is given of Tits' theorem that a finite subgroup of a Coxeter group must be contained in a conjugate of a finite parabolic subgroup. The final lecture gives a brief indication of the connections between Coxeter groups and buildings and BN-pairs.

Key phrases

Coxeter group. Presentation of a group. Real vector space. Bilinear form.

AMS Subject Classification (1991)

Primary: 20F55


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