A positivity conjecture on the structure constants of shifted Jack functions

We consider Jack polynomials $J_{\lambda }$ and their shifted analogue J^#_\lambda. In 1989, Stanley conjectured that $⟨J_{\mu }{J}_{\nu },J_{\lambda }⟩$ is a polynomial with nonnegative coefficients in the parameter $\alpha$. In this note, we extend this conjecture to the case of shifted Jack polynomials.