  In the genus expansion of the HOMFLY polynomials their representation
dependence is naturally captured by symmetric group characters. This
immediately implies that the Ooguri-Vafa partition function (OVPF) is a Hurwitz
tau-function. In the planar limit involving factorizable special polynomials,
it is actually a trivial exponential tau-function. In fact, in the double
scaling Kashaev limit (the one associated with the volume conjecture) dominant
in the genus expansion are terms associated with the symmetric representations
and with the integrability preserving Casimir operators, though we stop one
step from converting this fact into a clear statement about the OVPF behavior
in the vicinity of q=1. Instead, we explain that the genus expansion provides a
hierarchical decomposition of the Hurwitz tau-function, similar to the
Takasaki-Takebe expansion of the KP tau-functions. This analogy can be helpful
to develop a substitute for the universal Grassmannian description in the
Hurwitz tau-functions.
