The perspective of Kac-Schwarz operators is introduced to the authors&#039;<br />
previous work on the quantum mirror curves of topological string theory in<br />
strip geometry and closed topological vertex. Open string amplitudes on each<br />
leg of the web diagram of such geometry can be packed into a multi-variate<br />
generating function. This generating function turns out to be a tau function of<br />
the KP hierarchy. The tau function has a fermionic expression, from which one<br />
finds a vector $|W\rangle$ in the fermionic Fock space that represents a point<br />
$W$ of the Sato Grassmannian. $|W\rangle$ is generated from the vacuum vector<br />
$|0\rangle$ by an operator $g$ on the Fock space. $g$ determines an operator<br />
$G$ on the space $V = \mathbb{C}((x))$ of Laurent series in which $W$ is<br />
realized as a linear subspace. $G$ generates an admissible basis<br />
$\{\Phi_j(x)\}_{j=0}^\infty$ of $W$. $q$-difference analogues $A$, $B$ of<br />
Kac-Schwarz operators are defined with the aid of $G$. $\Phi_j(x)$&#039;s satisfy<br />
the linear equations $A\Phi_j(x) = q^j\Phi_j(x)$, $B\Phi_j(x) = \Phi_{j+1}(x)$.<br />
The lowest equation $A\Phi_0(x) = \Phi_0(x)$ reproduces the quantum mirror<br />
curve in the authors&#039; previous work.