Affine Action

(Representation Theory Of Lie Algebra)


Representation Theory Of Lie Algebra
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What is Affine action?

Let be the Weyl group of a semisimple Lie algebra (associate to fixed choice of a Cartan subalgebra ). Assume that a set of simple roots in is chosen. The affine action (also called the dot action) of the Weyl group on the space is where is the sum of all fundamental weights, or, equivalently, the half of the sum of all positive roots.

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representation theory of lie algebra


Dot action

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