  We prove the abelian-nonabelian correspondence for quasimap $I$-functions.
That is, if $Z$ is an affine l.c.i. variety with an action by a complex
reductive group $G$, we prove an explicit formula relating the quasimap
$I$-functions of the GIT quotients $Z//_{\theta} G$ and $Z//_{\theta} T$ where
$T$ is a maximal torus of $G$. We apply the formula to compute the
$J$-functions of some Grassmannian bundles on Grassmannian varieties and
Calabi-Yau hypersurfaces in them.
