  In this paper we introduce a new family of the KP tau-functions. This family
can be described by a deformation of the generalized Kontsevich matrix model.
We prove that the simplest representative of this family describes a generating
function of the cubic Hodge integrals satisfying the Calabi-Yau condition, and
claim that the whole family describes its generalization for the higher spin
cases. To investigate this family we construct a new description of the Sato
Grassmannian in terms of a canonical pair of the Kac-Schwarz operators.
