Is there an expression for Jack polynomials in terms of the power sum basis? The Jack polynomials are the 1-parameter family of eigenfunctions of the differential operator:
$$
D_\alpha = \frac{\alpha}{2} \sum_{i} x_i^2 \frac{\partial^2}{\partial x_i^2} + \sum_{i \neq j} \frac{x_i}{x_i - x_j} \frac{\partial}{\partial x_i}
$$
I know that for the Jack polynomial $J_\lambda$,
$$
J_\lambda = m_\lambda + \sum_{\mu < \lambda} c_{\lambda\mu}m_\mu
$$
for some constants $c_{\lambda \mu}$, and where $m_\lambda$ is the symmetric polynomial given by the partition $\lambda$.
Also, for each symmetric polynomial $m_{\lambda}$,
$$
m_\lambda = p_\lambda + \sum_{\mu > \lambda} a_{\lambda \mu} p_\mu
$$
again for some constants $a_{\lambda \mu}$ and where $p_\lambda = p_{\lambda_1} p_{\lambda_2} p_{\lambda_3} \cdots$ is the product of power sums given by the parts of $\lambda$.
So already I can see that the general expression would be quite complicated, as the Jacks are expressed down the dominance ordering of partitions with the $m_\lambda$s, but the $m_\lambda$s are expressed up the dominance ordering in the $p_\lambda$s
Even in restricted cases of the parameter used to define the Jack polynomials would be good, if there is an easier case. For instance I know that when $0< \alpha < 1$, each $c_{\lambda\mu}$ is a positive integer (rational?).
((Really what I am after is the coefficient on the highest-weighted $p_\lambda$ appearing in the Jack polynomial, so any pointers towards this would be ok too))

You might want to look up Hanlon's conjecture. It is basically gives these "Jack characters" in a quite nice form. 
Also, see corollary 4.3.1 in here, which gives a power-sum expansion of the Jack polynomials.
