Department of Mathematics, Dietrich School of Arts and Sciences, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260, U.S.A.
Abstract
We consider the semigroup $S$ of highest weights appearing in tensor powers $V^{\otimes k}$ 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 $V^{\otimes k}$ in terms of the volume of this polytope.
Kaveh, K. (2015). A remark on asymptotic enumeration of highest weights in tensor powers of a representation. Bulletin of the Iranian Mathematical Society, 41(3), 639-646.
MLA
K. Kaveh. "A remark on asymptotic enumeration of highest weights in tensor powers of a representation". Bulletin of the Iranian Mathematical Society, 41, 3, 2015, 639-646.
HARVARD
Kaveh, K. (2015). 'A remark on asymptotic enumeration of highest weights in tensor powers of a representation', Bulletin of the Iranian Mathematical Society, 41(3), pp. 639-646.
VANCOUVER
Kaveh, K. A remark on asymptotic enumeration of highest weights in tensor powers of a representation. Bulletin of the Iranian Mathematical Society, 2015; 41(3): 639-646.
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