Abelianization and Quantum Lefschetz for Orbifold Quasimap $I$-Functions

TL;DR

This paper establishes formulas connecting the small quasimap I-functions of GIT quotients by a reductive group and its maximal torus, providing explicit formulas in certain cases, advancing the understanding of orbifold quasimap invariants.

Contribution

It introduces new formulas relating quasimap I-functions of GIT quotients under a reductive group and its torus, including explicit formulas for vector space cases.

Findings

Derived formulas relating I-functions of different GIT quotients.

Provided explicit formulas for small I-functions in vector space cases.

Enhanced computational tools for orbifold quasimap invariants.

Abstract

Let $Y$ be a complete intersection in an affine variety $X$, with action by a complex reductive group $G$. Let $T \subset G$ be a maximal torus. A character $\theta$ of $G$ defines GIT quotients $Y//_\theta G$ and $X//_\theta T$. We prove formulas relating the small quasimap I-function of $Y//_\theta G$ to that of $X//_\theta T$. When $X$ is a vector space, this provides a completely explicit formula for the small $I$-function of $Y//_\theta G$.