  The structure of filtered algebras of Grothendieck's differential operators
of truncated polynomials in one variable and graded Poisson algebras of their
principal symbols is explicitly determined. A related infinitesimal-birational
duality realized by a Springer type resolution of singularities and the Fourier
transformation is presented. This algebro-geometrical duality is quantized in
appropriate sense and its quantum origin is explained.
