Residue formula for flag manifold of type A from wall-crossing

We consider equivariant integrals on flag manifolds of type A. Using a computational method inspired by the theory of wall-crossing formulas by Takuro Mochizuki, we re-prove residue formulas for equivariant integrals given by Weber and Zielenkiewicz. As an application, we give the determinantal formula of the Grothendieck polynomial by properly setting K theory classes.