The Abelian-Nonabelian Correspondence for $I$-functions

Abstract

We prove the abelian-nonabelian correspondence for quasimap $I$-functions. That is, if $Z$ is an affine l.c.i. variety with 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.

Strengthened the main result include quotients of affine varieties. The paper is almost entirely rewritten

References in corpus (3)

• A Luna étale slice theorem for algebraic stacks
• A Mathematical Theory of the Gauged Linear Sigma Model
• Virtual cycles of stable (quasi)-maps with fields

Cited by in corpus (4)

• A rim-hook rule for quiver flag varieties
• Nonabelian mirrors and Gromov-Witten invariants
• Four dimensional Fano quiver flag zero loci (with an appendix by T. Coates, E. Kalashnikov, and A. Kasprzyk)
• Virtual Coulomb branch and vertex functions