The Weyl group of a root system , where is a Euclidean vector space, is the subgroup of generated by reflection in the hyperplanes perpendicular to the roots. The map of reflection in a root 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 , where is the minimal number of reflections in simple roots that can be written as. This is also the number of positive roots that takes to negative roots.
|Date of creation||2013-03-22 13:11:52|
|Last modified on||2013-03-22 13:11:52|
|Last modified by||mathcam (2727)|