A product formula for certain coefficients of Jack polynomials

In this talk, we will discuss Jack symmetric functions, which generalize several classical families of symmetric functions, and are further generalized by Macdonald polynomials. In 1989, Richard Stanley conjectured that certain coefficients which appear when a product of two Jack polynomials is expanded as a sum can be described combinatorially in terms of weighted hooks of Young diagrams. I will outline a proof of Stanley's conjecture for a sub-family of Jack polynomials. These results also extend to the corresponding sub-family of Macdonald polynomials.