Root system

Dual root system

Let Φ be a root system. To any root 𝛼 ∈Φ one associated a coroot geo

𝛼∨=2𝛼(𝛼,𝛼)

and the set of all coroots Φ∨ forms the dual root system, whose Weyl group is canonically isomorphic to that of Φ.¹

Proof

proof

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develop | en | SemBr

Footnotes

1. 1972. Introduction to Lie algebras and representation theory, §9.2, p. 43 ↩