A remark on asymptotic enumeration of highest weights in tensor powers of a representation
arXiv:1002.1984
Abstract
We consider the semigroup S of highest weights appearing in tensor powers V^k of a finite 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.
Minor corrections, title slightly changed, an example added. 7 pages