Jack polynomials (or Jack symmetric functions) form a class of symmetric functions labelled by a partition and a parameter ; by a result of I. G. Macdonald, they form a family of orthogonal polynomials. Jack polynomials can be defined as eigenfunctions of certain Laplac/Beltrami type operator coming in the theory of Calogero integrable systems and in random matrix theory. If the Jack polynomials become Schur polynomials.
Henry Jack, A class of symmetric polynomials with a parameter, Proc. Roy. Soc. Edinburgh Sec. A: Math. Phys. Sci. 69, 1-18, 1969-70, MR289462; reprinted in: Contemp. Math. 417, Jack, Hall-Littlewood and Macdonald polynomials, 57–74, Amer. Math. Soc. 2006
H. Jack, A class of polynomials in search of a definition, or the symmetric group parametrized, in: Jack, Hall-Littlewood and Macdonald polynomials, 75–106, AMS 2006