  This paper addresses the issue of integrable structures in topological string
theory on generalized conifolds. Open string amplitudes of this theory can be
expressed as the matrix elements of an operator on the Fock space of 2D charged
free fermion fields. The generating function of these amplitudes with respect
to the product of two independent Schur functions becomes a tau function of the
2D Toda hierarchy. The associated Lax operators turn out to have a particular
factorized form. This factorized form of the Lax operators characterizes a
generalization of the Ablowitz-Ladik hierarchy embedded in the 2D Toda
hierarchy. The generalized Ablowitz-Ladik hierarchy is thus identified as a
fundamental integrable structure of topological string theory on the
generalized conifolds.
