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Trşed to check in French wikipedia but they don't have the concept |
''X'' != weight lattice P, rather: Q (root lattice) \subseteq X \subseteq P with strict inclusions in general! |
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* For each <math>\alpha</math>, the map <math>x\mapsto x-(x,\alpha^\vee)\alpha</math> induces an automorphism of the root datum (in other words it maps <math>\Phi</math> to <math>\Phi</math> and the induced action on <math>X_\ast</math> maps <math>\Phi^\vee</math> to <math>\Phi^\vee</math>)
The elements of <math>\Phi</math> are called the '''roots''' of the root datum, and the elements of <math>\Phi^\vee</math> are called the '''coroots
If <math>\Phi</math> does not contain <math>2\alpha</math> for any <math>\alpha\in\Phi</math>, then the root datum is called '''reduced'''.
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