I know this might be a very elementary question. But I could not find the original definition of Extreme(or Extremal)vectors of some weights $\lambda$(fixed the $w\in W$,where $W$ is Weyl group)


I am looking for definition for Extreme vector for finite dimensional Lie algebra and Affine Lie algebra. I found a paper saying :"Extreme vector verifies Weyl Character formula" What does it mean?


I am looking for reference talking about this concept. Thanks in advance


EDIT: I guess it is just highest weight vector, but I am not sure



What is Extreme/Extremal vector according to some weights
Usually "extremal weight" means a weight in the Weyl group orbit of the highest, and I would interpret "extremal vector" as an element of said weight space.


