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==Definition==
A '''root datum''' consists of a quadruple
:(''X''<sup>*</sup>, Δ, ''X''<sub>*</sub>, Δ<sup>v</sup>),
where
*''X''<sup>*</sup> and ''X''<sub>*</sub> are free abelian groups of finite [[Rank (linear algebra)|rank]] together with a perfect pairing between them with values in '''Z''' which we denote by ( , ) (in other words, each is identified with the [[dual lattice]] of the other).
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