Harmonic functions on multiplicative graphs and interpolation polynomials

Details Harmonic functions on multiplicative graphs and interpolation polynomials Harmonic functions on multiplicative graphs and interpolation polynomials

1999-12-15

arxiv.org/abs/math/9912124v1

Electronic Journal of Combinatorics 7 (2000), paper R28

Mathematics

Combinatorics

AMSTeX, 35 pages

Scientific paper

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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