  We present a conjecture that the universal enveloping algebra of differential
operators $\frac{\p}{\p t_k}$ over $\mathbb{C}$ coincides in the origin with
the universal enveloping algebra of the (Borel subalgebra of) Virasoro
generators from the Kontsevich model. Thus, we can decompose any
(pseudo)differential operator to a combination of the Virasoro operators. Using
this decomposition we present the r.h.s. of the Givental formula
math.AG/0008067 as a constant part of the differential operator we introduce.
In the case of $\mathbb{CP}^1$ studied in hep-th/0103254, the l.h.s. of the
Givental formula is a unit, which imposes certain constraints on this
differential operator. We explicitly check that these constraints are correct
up to $O(q^4)$. We also propose a conjecture of factorization modulo Hirota
equation of the differential operator introduced and check this conjecture with
the same accuracy.
