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

• Type: Journal
• Year: 2000
• Where: COMBINATORICS
• Authors: Alexei Borodin, Grigori Olshanski
• Keywords: Certain Graded Graphs, COMBINATORICS 2000, Jack Symmetric Functions, Nonnegative Harmonic Functions