The Abelian–Nonabelian Correspondence for I-Functions

Abstract

Abstract 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 geometric invariant theory quotients $Z\mathord{/\mkern -6mu/}_{\theta } G$ and $Z\mathord{/\mkern -6mu/}_{\theta } T$ 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.