Dual Root System and Coroots
See also: Langlands dual groupIf Φ is a root system in V, the coroot αV of a root α is defined by
The set of coroots also forms a root system ΦV in V, called the dual root system (or sometimes inverse root system). By definition, αV V = α, so that Φ is the dual root system of ΦV. The lattice in V spanned by ΦV is called the coroot lattice. Both Φ and ΦV have the same Weyl group W and, for s in W,
If Δ is a set of simple roots for Φ, then ΔV is a set of simple roots for ΦV.
Read more about this topic: Root System
Famous quotes containing the words dual, root and/or system:
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—Ralph Waldo Emerson (1803–1882)
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—Doris Lessing (b. 1919)