  We use the Jack symmetric functions as a basis of the Fock space, and study
the action of the Virasoro generators $L_n$. We calculate explicitly the matrix
elements of $L_n$ with respect to the Jack-basis. A combinatorial procedure
which produces these matrix elements is conjectured. As a limiting case of the
formula, we obtain a Pieri-type formula which represents a product of a power
sum and a Jack symmetric function as a sum of Jack symmetric functions. Also, a
similar expansion was found for the case when we differentiate the Jack
symmetric functions with respect to power sums. As an application of our
Jack-basis representation, a new diagrammatic interpretation is presented, why
the singular vectors of the Virasoro algebra are proportional to the Jack
symmetric functions with rectangular diagrams. We also propose a natural
normalization of the singular vectors in the Verma module, and determine the
coefficients which appear after bosonization in front of the Jack symmetric
functions.
