  Let $K$ be an infinite field of characteristic $p>0$ and let $\lambda, \mu$
be partitions, where $\mu$ has two parts. We find sufficient arithmetic
conditions 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 the
corresponding homomorphism spaces have dimension at least 2.
