Principal hierarchies of infinite-dimensional Frobenius manifolds: The extended 2D Toda lattice

We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/∞$0/\infty$ respectively, which extends the dispersionless 2D Toda hierarchy of Takasaki and Takebe. Then we construct the deformed flat connection of the infinite-dimensional Frobenius manifold _M0$M_0$ introduced by Carlet, Dubrovin and Mertens (2011) [3] and, by explicitly solving the deformed flatness equations, we prove that the extended 2D Toda hierarchy coincides with principal hierarchy of _M0$M_0$.