Weyl chamber

Let E be a Euclidean vector space, RβŠ‚E a root systemMathworldPlanetmath, and R+βŠ‚R a choice of positive roots. We define the positive Weyl chamber (relative to R+) to be the closed set

π’ž={u∈E∣(u,Ξ±)β‰₯0⁒ for all ⁒α∈R+}.

A weight which lies inside the positive Weyl chamber is called dominant.

The interior of π’ž is a fundamental domain for the action of the Weyl groupMathworldPlanetmathPlanetmath on E. The image w⁒(π’ž) of π’ž under the any element w of the Weyl group is called a Weyl chamber. The Weyl group W acts simply transitively on the set of Weyl chambers.

Title Weyl chamber
Canonical name WeylChamber
Date of creation 2013-03-22 13:12:00
Last modified on 2013-03-22 13:12:00
Owner rmilson (146)
Last modified by rmilson (146)
Numerical id 8
Author rmilson (146)
Entry type Definition
Classification msc 17B20
Defines positive Weyl chamber
Defines dominant weight