Jack symmetric polynomials are known to be generalizations of Schur functions $\chi\_\lambda$, for which powerful Weyl determinant formulas are known. 
Are there any generalizations of two determinant formulas for general Jack symmetric $P^\alpha\_\lambda(x)$ functions? 


The first determinant (Jacobi-Trudi) formula represents the character of the irrep GL(N) given by the partition $\lambda$ 
$$
\chi\_\lambda(x)=\det\_{i,j} s\_{\lambda\_i-i+j}
$$
where $s\_k$ are elementary Schur function
and the second one gives the same function as determinant
$$
\chi\_\lambda(x)=\frac{\det\_{i,j} x\_i^{\lambda\_j+N-j}}{\det\_{i,j} x\_i^{N-j}}
$$
Jack symmetric polynomials are natural generalizations of Schur polynomials, and probably, to operate with them it would be useful to have as simple as possible analogs of Weyl formulas.



Jack polynomials as determinants
A natural analog would be a representation of the Jack polynomial as an alternating sum of eigenfunctions of the Calogero-Sutherland operator over an orbit of the symmetric group. This can be done even in the q-deformed case (i.e. for Macdonald polynomials and Macdonald operators). Such formula was conjectured by Felder and Varchenko and proved in the paper 
arXiv:q-alg/9603022, see formula (5-5). 


