Harmonic functions on multiplicative graphs and interpolation polynomials
Combinatorics
2016-09-07 v1 Representation Theory
Abstract
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.
Cite
@article{arxiv.math/9912124,
title = {Harmonic functions on multiplicative graphs and interpolation polynomials},
author = {Alexei Borodin and Grigori Olshanski},
journal= {arXiv preprint arXiv:math/9912124},
year = {2016}
}
Comments
AMSTeX, 35 pages