  The universal enveloping algebra U(g) of a Lie algebra g acts on its
representation ring R through D(R), the ring of differential operators on R. A
quantised universal enveloping algebra (or "quantum group") is a deformation of
a universal enveloping algebra and acts not through the differential operators
of its representation ring but through the quantised differential operators of
its representation ring. We present this situation for the quantum group of
sl_2.
