Anisotropic Young Diagrams and Jack Symmetric Functions

Λ:λրΛ(cα(b) + u)(cα(b) + v)κα(λ,Λ)φ(Λ) = (nα + uv) φ(λ), where cα(b) is the α-content of a new box b = Λ \ λ. If α = 1, this identity implies the existence of an interesting family of positive definite central functions on the infinite symmetric group. The approach is based on the interpretation of a Young diagram as a pair of interlacing sequences, so that analytic techniques may be used to solve combinatorial problems. We show that when dealing with Jack polynomials Pλ(x;α), it makes sense to consider anisotropic Young diagrams made of rectangular boxes of size 1 × α.