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A remark on asymptotic enumeration of highest weights in tensor powers of a representation

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.

preprint2015arXivOpen access
Kiumars Kaveh
math.COmath.RT
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Kiumars Kaveh

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