  This work takes place over a conformally flat spin manifold (M,g). We prove
existence and uniqueness of the conformally equivariant quantization valued in
spinor differential operators, and provide an explicit formula for it when
restricted to first order operators. The Poisson algebra of symbols is realized
as a space of functions on the supercotangent bundle, endowed with a symplectic
form depending on the metric g. It admits two different actions of the
conformal Lie algebra, one tensorial and one Hamiltonian. They are intertwined
by the uniquely defined conformally equivariant superization, for which an
explicit formula is given. This map allows us to classify all the conformal
supercharges of the spinning particle in terms of conformal Killing tensors
with mixed symmetry, generated by the totally symmetric and skew-symmetric
ones. Higher symmetries of the Dirac operator are obtained by quantization of
the conformal supercharges.
