The Abelian–Nonabelian Correspondence for <i>I</i>-Functions

Abstract We prove the abelian–nonabelian correspondence for quasimap $I$-functions. That is, if $Z$ is an affine l.c.i. variety with action by a complex reductive group $G$, we explicit formula relating $I$-functions of geometric invariant theory quotients $Z\mathord{/\mkern -6mu/}_{\theta } G$ and T$ where $T$ maximal torus $G$. apply to compute $J$-functions some Grassmannian bundles on varieties Calabi–Yau hypersurfaces in them.