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Affine action : ウィキペディア英語版
Affine action
Let W be the Weyl group of a semisimple Lie algebra \mathfrak (associate to fixed choice of a Cartan subalgebra \mathfrak). Assume that a set of simple roots in \mathfrak^
* is chosen.
The ''affine action'' (also called the ''dot action'') of the Weyl group on the space \mathfrak^
* is
:w\cdot \lambda:=w(\lambda+\delta)-\delta
where \delta is the sum of all fundamental weights, or, equivalently, the half of the sum of all positive roots.
==References==

* .

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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