  The present work is much motivated by finding an explicit way in the
construction of the Jack symmetric function, which is the spectrum generating
function for the Calogero-Sutherland(CS) model. To accomplish this work, the
hidden Virasoro structure in the CS model is much explored. In particular, we
found that the Virasoro singular vectors form a skew hierarchy in the CS model.
Literally, skew is analogous to coset, but here specifically refer to the
operation on the Young tableaux. In fact, based on the construction of the
Virasoro singular vectors, this hierarchical structure can be used to give a
complete construction of the CS states, i.e. the Jack symmetric functions,
recursively. The construction is given both in operator formalism as well as in
integral representation. This new integral representation for the Jack
symmetric functions may shed some insights on the spectrum constructions for
the other integrable systems.
