Big $I$-functions

Abstract

We introduce a new big $I$-function for certain GIT quotients $W/\!\!/\mathbf{G}$ using the quasimap graph space from infinitesimally pointed $\mathbb{P}^1$ to the stack quotient $[W/\mathbf{G}]$. This big $I$-function is expressible by the small $I$-function introduced in [6, 10]. The $I$-function conjecturally generates the Lagrangian cone of Gromov-Witten theory for $W/\!\!/\mathbf{G}$ defined by Givental. We prove the conjecture when $W/\!\!/\mathbf{G}$ has a torus action with good properties.