Abstract :
Abstract. We consider the semigroup S of highest weights appearing in
tensor powers V k of a nite dimensional representation V of a connected
reductive group. We describe the cone generated by S as the cone over the weight polytope of V intersected with the positive Weyl chamber. From this we get a description for the asymptotic of the number of highest weights appearing in V k in terms of the volume of this polytope.
Keywords :
moment polytope , weight polytope , semigroup of integral points , tensor power , Reductive group representation
