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

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 $Y/{/}_{\theta }G$.

Corrected an error in the statement of the quantum lefschetz theorem; also fixed the proof

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