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For any root datum (''X''<sup>*</sup>, Δ,''X''<sub>*</sub>, Δ<sup>v</sup>), we can define a '''dual root datum''' (''X''<sub>*</sub>, Δ<sup>v</sup>,''X''<sup>*</sup>, Δ) by switching the characters with the 1-parameter subgroups, and switching the roots with the coroots.
If ''G'' is a connected reductive algebraic group over the algebraically closed field ''K'', then its [[Langlands dual group]] <sup>''L''</sup>''G'' is the complex connected reductive group whose root datum is dual to that of ''G''.
==References==
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