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Weyl Chamber


A Weyl chamber of a root system is a connected component of the complement of its reflecting hyperplanes in the ambient real vector space. Choosing a set of positive roots determines a set of simple roots and the fundamental chamber

 C={x:<x,alpha>>0 for every chosen alpha}.

The Weyl group acts simply transitively on the Weyl chambers, and the closure of a chamber is a fundamental domain for this action.


See also

Coxeter Group, Fundamental Domain, Root System, Weyl Group

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References

Humphreys, J. E. Reflection Groups and Coxeter Groups. Cambridge, England: Cambridge University Press, 1990.

Cite this as:

Weisstein, Eric W. "Weyl Chamber." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WeylChamber.html

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