Virasoro constraints for Kontsevich-Hurwitz partition function

In [ 1, 2] M. Kazarian and S. Lando found a 1-parametric interpolation between Kontsevich and Hurwitz partition functions, which entirely lies within the space of KP tau-functions. In [3] V. Bouchard and M. Marino suggested that this interpolation satisfies some deformed Virasoro constraints. However, they described the constraints in a somewhat sophisticated form of AMM-Eynard equations [4-7] for the rather involved Lambert spectral curve. Here we present the relevant family of Virasoro constraints explicitly. They differ from the conventional continuous Virasoro constraints in the simplest possible way: by a constant shift u(2)/24 L- 1 operator, where u is an interpolation parameter between Kontsevich and Hurwitz models. This trivial modification of the string equation gives rise to the entire deformation which is a conjugation of the Virasoro constraints gives rise to the entire deformation which is a conjugationn of the Virasoro constraints (L) over cap (m) -> (U) over cap (L) over cap (m) (U) over cap (-1) and '' twists '' the partition function, Z(KH) = (U) over capZ(K). The conjugation (U) over cap = exp {u(2)/3((N) over cap (1) - (L) over cap (1)) + O(u(6))} = exp {u(2)/12 (Sigma(k) T-k partial derivative/partial derivative Tk+1 - g(2)/2 partial derivative(2) / partial derivative T-0(2)) + O(u(6))} is expressed through the previously unnoticed operators like (N) over cap (1) = Sigma(k)(k + 1)T-2(k)partial derivative/partial derivative Tk+1 which annihilate the quasiclassical (planar free energy F-K((0)) of the Kontsevich model. but do not belong to the symmetry group GL(infinity) of the universal Grassmannian.