Content deleted Content added
Rewritten in LaTeX + Name "(Co)weights" for elements of X^* (resp. X_*) |
|||
Line 10:
* 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'''. The elements of <math>X^\ast</math> are sometimes called '''[[Weight_(representation_theory)|weights]]''' and those of <math>X_\ast</math> accordingly '''coweights'''.
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'''.
| |||