We fix a simple finite-dimensional complex Lie algebra \g and a simple Lie subalgebra \a of \g induced by a closed subset of positive roots. If one considers the restriction of a given finite-dimensional simple \g-module to \a, then the component of the highest weight vector is a simple \a-module. If we generalize this to (generalized) current algebras, we obtain an analog picture. What happens to the restriction of local and global Weyl modules to the highest weight vector component?

Here the answer depends on \g, \a and the highest weight of the Weyl module, but we will give necessary and sufficient conditions such that this component is again a local or global Weyl module.