  In the paper there are investigated various approximate representations of
the infinite dimensional $\Bbb Z$--graded Lie algebras: the Witt algebra of all
Laurent polynomial vector fields on a circle and its one-dimensional nontrivial
central extension, the Virasoro algebra, by the infinite dimensional hidden
symmetries in the Verma modules over the Lie algebra $\sl(2,C)$. There are
considered as asymptotic representations "$mod O(\hbar^n)$" and representations
up to a class $\frak S$ of operators (compact operators, Hilbert-Schmidt
operators and finite-rank operators) as cases, which combine both types of
approximations and in these cases an effect of noncommutativity of the order of
their perform is explicated, that perhaps is underlied by a more general
fundamental fact of deviations between the asymptotical theory of
pseudodifferential operators and the pseudodifferential calculus on the
asymptotic manifolds.
