Twisted GL_n Loop Group Orbit and Solutions of the WDVV Equations

We show that all (n-component) KP tau-functions, which are related to the twisted loop group of $G{L}_n$, give solutions of the Darboux-Egoroff system of PDE’s. Using the Geometry of the Grassmannian we construct from the corresponding wave function the deformed flat coordinates of the Egoroff metric and from this the corresponding solution of the Witten-Dijkgraaf-E. Verlinde-H. Verlinde equations.