For an infinite field k of positive characteristic, we determine all homomorphisms between Weyl modules for $G{L}_n(k)$, where one of the partitions is a hook. As a consequence we obtain a non-vanishing result concerning homomorphisms between Weyl modules for algebraic groups of type B, C and D when one of the partitions is a hook.

中文翻译：

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关于钩子 Weyl 模块的同态

对于具有正特征的无穷场k，我们确定 Weyl 模之间的所有同态$G{升}_n(克)$，其中一个分区是一个钩子。因此，当分区之一是钩子时，我们获得了关于B、C和D类型代数群的 Weyl 模之间的同态的非零结果。