  Let g be a semisimple Lie algebra over an algebraically closed field K of
characteristic 0 and O be a nilpotent orbit in g. Then Orb is a symplectic
algebraic variety and one can ask whether it is possible to quantize $\Orb$ (in
an appropriate sense) and, if so, how to classify the quantizations. On the
other hand, for the pair (g,O) one can construct an associative algebra W
called a (finite) W-algebra. The goal of this paper is to clarify a
relationship between quantizations of O (and of its coverings) and
1-dimensional W-modules. In the first approximation, our result is that there
is a one-to-one correspondence between the two. The result is not new: it was
discovered (in a different form) by Moeglin in the 80's.
