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

Kiumars Kaveh

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

Representation Theory 2015-08-06 v2 Combinatorics

Authors: Kiumars Kaveh

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.

Keywords

highest weight tensor power reductive group weight polytope Weyl chamber asymptotic enumeration

Cite

@article{arxiv.1002.1984,
  title  = {A remark on asymptotic enumeration of highest weights in tensor powers of a representation},
  author = {Kiumars Kaveh},
  journal= {arXiv preprint arXiv:1002.1984},
  year   = {2015}
}

Comments

Minor corrections, title slightly changed, an example added. 7 pages

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