Weyl group
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.
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 |