Let G be a simple algebraic group in defining characteristic $p>0$, and let V be an irreducible G-module which is the tensor product of exactly two non-trivial modules. We obtain a criterion for V to have the zero weight. In addition, we provide a uniform criterion for an irreducible representation of a simple Lie algebra over the complex numbers to have a multiple of a prescribed fundamental weight.

中文翻译：

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简单代数组的张量可分解不可约表示中的权重为零

令G为定义特征的简单代数群$p>0$，令V为不可约G模，它是恰好两个非平凡模量的张量积。我们获得一个准则，使V的权重为零。另外，我们提供了一个简单的李代数在复数上的不可约表示的统一准则，该复数具有规定的基本权重的倍数。