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Harmonic functions on multiplicative graphs and interpolation polynomials

We construct examples of nonnegative harmonic functions on certain graded graphs: the Young lattice and its generalizations. Such functions first emerged in harmonic analysis on the infinite symmetric group. Our method relies on multivariate interpolation polynomials associated with Schur's S and P functions and with Jack symmetric functions. As a by-product, we compute certain Selberg-type integrals.

preprint1999arXivOpen access
Alexei BorodinGrigori Olshanski
math.COmath.RT
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Alexei BorodinGrigori Olshanski

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