- References
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.
References
- {{citation|first1=Robert J.|last1=Baston|first2=Michael G.|last2=Eastwood|authorlink2=Michael Eastwood|title=The Penrose Transform: its Interaction with Representation Theory|publisher=Oxford University Press|year=1989}}.
1 : Representation theory of Lie algebras
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