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arXiv · 1508.03071

Components of V(\rho)\otimes V(\rho)

Shrawan Kumar
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Abstract

Kostant asked the following question: Let $\mathfrak{g}$ be a simple Lie algebra over the complex numbers. Let $\lambda$ be a dominant integral weight. Then, $V(\lambda)$ is a component of $ V(\rho)\otimes V(\rho)$ if and only if $\lambda \leq 2\rho$ under the usual Bruhat-Chevalley order on the set of weights. We give an affirmative answer to this question up to a saturation factor. In particular, the question is answered affirmatively for the special linear Lie algebras due to the Saturation Theorem of Knutson-Tao.

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Shrawan Kumar. 2015-08-12. Components of V(\rho)\otimes V(\rho). https://arxiv.org/abs/1508.03071

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