# Introduction to Coxeter groups

## Author

**Robert B. Howlett**

## Status

Research Report 97-6

Lectures delivered at the A.N.U. Geometric Group Theory Workshop

Date: February 1996

## Abstract

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

Secondary:

## Content

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