论文标题
简单代数组的张量可分解不可约合表示的重量为零
Weight zero in tensor-decomposable irreducible representations of simple algebraic groups
论文作者
论文摘要
让$ g $是定义特征$ p> 0 $的简单代数群，而让$ v $是不可约$ g $ - 模块，它是两个非平凡模块的张量产品。我们获得了$ V $的标准，以使重量为零。此外，我们提供了一个统一的标准，用于对复数的简单代数的不可约表示，以具有规定的基本权重的倍数。
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.
