  The paper \cite{BM} proposed a construction of a twisted representation of
the lattice vertex algebra corresponding to the Milnor lattice of a simple
singularity. The main difficulty in extending the above construction to an
arbitrary isolated singularity is in the so called {\em phase factors} -- the
scalar functions produced by composing two vertex operators. They are certain
family of multivalued analytic functions on the space of miniversal
deformations. The first result in this paper is an explicit formula for the
unperturbed phase factors in terms of the classical monodromy operator and the
polylogorithm functions. Our second result is that with respect to the
deformation parameters the phase factors are analytic functions on the
monodromy covering space.
