Geodesic
Harmonic functions on multiplicative graphs and interpolation polynomials
The electronic journal of combinatorics, Tome 7 (2000)
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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.
DOI : 10.37236/1506
Classification : 05E10, 31C20, 60C05
Mots-clés : Young graph, Jack graph, Kingman graph, Schur graph, Young branching, harmonic functions, Young lattice, multivariate interpolation polynomials, symmetric functions 
@article{10_37236_1506,
     author = {Alexei Borodin and Grigori Olshanski},
     title = {Harmonic functions on multiplicative graphs and interpolation polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2000},
     volume = {7},
     doi = {10.37236/1506},
     zbl = {0939.05082},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1506/}
}
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Alexei Borodin; Grigori Olshanski. Harmonic functions on multiplicative graphs and interpolation polynomials. The electronic journal of combinatorics, Tome 7 (2000). doi: 10.37236/1506

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