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In this paper we introduce a new family of the KP tau-functions. This familycan be described by a deformation of the generalized Kontsevich matrix model.We prove that the simplest representative of this family describes a generatingfunction of the cubic Hodge integrals satisfying the Calabi-Yau condition, andclaim that the whole family describes its generalization for the higher spincases. To investigate this family we construct a new description of the SatoGrassmannian in terms of a canonical pair of the Kac-Schwarz operators.

KP integrability of triple Hodge integrals. II. Generalized Kontsevich matrix model