Quasimap I-function conjecture for the Gromov–Witten Lagrangian cone

Let $E\sslash \textbf{G}$ be the relevant GIT quotient, let $I(\mathbf{t},z)$ be the quasimap I-function, let $P^Q(\mathbf{t},z)$ be the corresponding quasimap input, and let $P(\mathbf{t},z)$ and $\tau(\mathbf{t})$ be the power-series element and change of variables constructed in the paper. Let $S^Q_{\mathbf{t}}(z)$ and $S_{\mathbf{t}}(z)$ denote the quasimap and Gromov–Witten S-operators. Quasimap I-function conjecture.

$$I(\mathbf{t},z)=S^Q_{\mathbf{t}}(z)(P^Q(\mathbf{t},z))=S_{\tau(\mathbf{t})}(z)(P(\tau(\mathbf{t}),z)).$$

In particular, $I$ lies on the Lagrangian cone of the Gromov–Witten theory of $E\sslash \textbf{G}$. The surrounding argument constructs $P$ and $\tau$ inductively to establish the stated identity, so the conjectural content is the resulting cone property and its interpretation as a quasimap/Gromov–Witten comparison.