  In Alexandrov's work \cite{al2, al3} it has been shown that the extended
partition function $\exp(F^{o,ext}+F^c)$ introduced by Buryak in \cite{bu, bu2}
is a tau-function of the KP hierarchy. In this work, we compute the affine
coordinates of this tau-function on the Sato Grassmannian, and rewrite the
Virasoro constraints as recursions for the affine coordinates in the fermionic
picture. As applications we derive some formulas for the extended partition
function and the connected $n$-point functions using methods developed by Zhou
in \cite{zhou1} based on the boson-fermion correspondence.
