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Harmonic Functions on Multiplicative Graphs and Interpolation Polynomials

Borodin, Alexei and Olshanski, Grigori (2000) Harmonic Functions on Multiplicative Graphs and Interpolation Polynomials. Electronic Journal of Combinatorics, 7 (R28). ISSN 1077-8926.

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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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Additional Information:Submitted: November 22, 1999; Accepted: May 15, 2000. One of the authors (G.O.) was supported by the Russian Foundation for Basic Research under grant 98-01-00303.
Issue or Number:R28
Record Number:CaltechAUTHORS:BORejc00
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2614
Deposited By: Archive Administrator
Deposited On:12 Apr 2006
Last Modified:02 Oct 2019 22:55

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