On affine coordinates of the tau-function for open intersection numbers

In Alexandrov's work [4], [5] it has been shown that the extended partition function exp⁡(Fo,ext+Fc) introduced by Buryak in [14], [15] is a tau-function of KP hierarchy. this work, we compute affine coordinates on Sato Grassmannian, and rewrite Virasoro constraints as recursions for fermionic picture. As applications derive some formulas connected n-point functions using methods developed Zhou [48] based boson-fermion correspondence.