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{\bf Alexei Borodin and Grigori Olshanski}
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{\bf Harmonic Functions on Multiplicative Graphs and Interpolation
Polynomials}
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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.
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