Quantum curve and bilinear Fermionic form for the orbifold Gromov-Witten theory of $\mathbb{P}[r]$

Abstract

We construct the quantum curve for the Baker-Akhiezer function of the orbifold Gromov-Witten theory of the weighted projective line $\mathbb P[r]$. Furthermore, we deduce the explicit bilinear Fermionic formula for the (stationary) Gromov-Witten potential via the lifting operator constructed from the Baker-Akhiezer function.