Weyl group

The Weyl groupMathworldPlanetmathPlanetmath WR of a root systemMathworldPlanetmath RE, where E is a Euclidean vector space, is the subgroupMathworldPlanetmathPlanetmath of GL(E) generated by reflectionMathworldPlanetmath in the hyperplanesMathworldPlanetmathPlanetmath perpendicularMathworldPlanetmathPlanetmathPlanetmath to the roots. The map of reflection in a root α is given by


The Weyl group is generated by reflections in the simple roots for any choice of a set of positive roots. There is a well-defined length function :WR, where (w) is the minimal number of reflections in simple roots that w can be written as. This is also the number of positive roots that w takes to negative roots.

Title Weyl group
Canonical name WeylGroup
Date of creation 2013-03-22 13:11:52
Last modified on 2013-03-22 13:11:52
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 6
Author mathcam (2727)
Entry type Definition
Classification msc 17B20