Orthogonality of Jack polynomials in superspace
arXiv:math-ph/0509039 · doi:10.1016/j.aim.2006.10.004
Abstract
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 hep-th/0209074 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 math.CO/0509408
22 pages, this supersedes the second part of math.CO/0412306; (v2) 24 pages, title and abstract slightly modified, minor changes, typos corrected