Orthogonality of Jack polynomials in superspace

Jack polynomials in superspace, orthogonal with respect to a “combinatorial” scalar product, are constructed. They are shown to coincide with the Jack polynomials in superspace, orthogonal with respect to an “analytical” scalar product, introduced in [P. Desrosiers, L. Lapointe, P. Mathieu, Jack polynomials in superspace, Comm. Math. Phys. 242 (2003) 331–360] as eigenfunctions of a supersymmetric quantum mechanical many-body problem. The results of this article rely on generalizing (to include an extra parameter) the theory of classical symmetric functions in superspace developed recently in [P. Desrosiers, L. Lapointe, P. Mathieu, Classical symmetric functions in superspace, J. Algebraic Combin. 24 (2006) 209–238].