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Let $K$ be an infinite field of characteristic $p>0$ and let $\lambda, \mu$be partitions, where $\mu$ has two parts. We find sufficient arithmeticconditions on $p, \lambda, \mu$ for the existence of a nonzero homomorphism$\Delta(\lambda) \to \Delta (\mu)$ of Weyl modules for the general linear group$GL_n(K)$. Also for each $p$ we find sufficient conditions so that thecorresponding homomorphism spaces have dimension at least 2.

On homomorphisms into Weyl modules corresponding to partitions with two parts