  In this paper, we investigate a relation between the Givental group of rank
one and the Heisenberg-Virasoro symmetry group of the KP hierarchy. We prove,
that only a two-parameter family of the Givental operators can be identified
with elements of the Heisenberg-Virasoro symmetry group. This family describes
triple Hodge integrals satisfying the Calabi-Yau condition. Using the
identification of the elements of two groups we prove that the generating
function of triple Hodge integrals satisfying the Calabi-Yau condition and its
$\Theta$-version are tau-functions of the KP hierarchy. This generalizes the
result of Kazarian on KP integrability in the case of linear Hodge integrals.
