Singular vectors in term of Schur polynomials in conformal field theory

Abstract EN

We extended the singular vectors in term of Schur polynomials to the states (r ,s ) = (3, 4), (4, 4) and proved the general case (r,s) for the coeffecients of the singular vector,we used the relation between Calogero-Sutherlan Model and conformal theory at central charge (c = 1) to prove the rectangular shape of singular vectors in our formula,also we construct another recursion relation to calculate the coefficients of the singular vector.