Big I-functions

We introduce a new big I-function for certain GIT quotients W//G using the quasimap graph space from infinitesimally pointed $\mathbb{P}^1$ to the stack quotient [W/G]. This big I-function is expressible by the small I-function introduced in arXiv:0908.4446 [math.AG] and arXiv:1106.3724 [math.AG]. The I-function conjecturally generates the Lagrangian cone of Gromov-Witten theory for W//G defined by Givental. We prove the conjecture when W//G has a torus action with good properties.