Givental formula in terms of Virasoro operators

We present a conjecture that the universal enveloping algebra of differential operators ∂ ∂tk over C coincides 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 some combination of the Virasoro operators. We use this decomposition to present the r.h.s. of the Givental formula [1] as a constant part of some differential operator we introduce. In the case of CP studied in [2], the l.h.s. of the Givental formula is unit, which imposes constraints on this differential operator. We explicitly check these constraints are correct up to O(q). We also propose a conjecture of factorization properties of the differential operator introduced modulo Hirota equation and check this conjecture with the same accuracy.