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.Comment: AMSTeX, 35 page

Borodin, Alexei

Olshanski, Grigori

arXiv.org e-Print Archive

CiteSeerX

Caltech Authors

English

A new approach to representation theory of symmetric groups,

Algebro-geometric applications of Schur S- and Q-polynomials, Topics

Analogs and extensions of Selberg’s integral, q-Series and partitions

and permutation actions with quasi-invariant measure, Representation theory, dynamical systems, combinatorial and algorithmical methods

Anisotropic Young diagrams and Jack symmetric functions,

Asymptotic theory of characters of the symmetric group,

Automorphic actions of compact groups on operator algebras, Thesis,

Characters, factor representations and K-functor of the in symmetric group., Operator algebras and group representations,

Combinatorial examples in the theory of AF-algebras, Dierential geometry, Lie groups and mechanics X,

Die unzerlegbaren, positive{de Klassenfunktionen der abza¨hlbar unendlichen,

Dierence equations and symmetric polynomials de by their zeros,

Dimension of skew shifted Young diagrams and projective representations of the in symmetric group, Representation theory, dynamical systems, combinatorial and algorithmical methods

formula for Macdonald polynomials,

Frobenius{Schur functions,

Hall{Littlewood symmetric functions and orthogonal polynomials, Representation Theory and Dynamical Systems

Harmonic analysis of functions of several complex variables in the classical domains,

Harmonic analysis on the in symmetric group. A deformation of the regular representation,

Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras,

immanants and higher Capelli identities,

Jack polynomials, binomial formula, and applications, q-alg/9608020,

Lectures on Choquet’s theorem,

Macdonald polynomials: q-Integral representation and combinatorial formula,

Multiplicative central measures on the Schur graph, Representation theory, dynamical systems, combinatorial and algorithmical methods

Multiplicative distributions on Young graph, Representation theory, dynamical systems, combinatorial and algorithmical methods

On a Jacobi{Trudi identity for supersymmetric polynomials,

on partitions, point processes, and the hypergeometric kernel, to appear in

Point processes and the in symmetric group,

Point processes and the in symmetric group. Part I: The general formalism and the density function,

Point processes and the in symmetric group. Part II: Higher correlation functions,

Point processes and the in symmetric group. Part III: Fermion point processes,

Point processes and the in symmetric group. Part IV: Matrix Whittaker kernel,

Point processes and the in symmetric group. Part V: Analysis of the matrix Whittaker kernel,

Polynomial functions on the set of Young diagrams, Comptes Rendus Acad. Sci. Paris Ser.

Population Genetics Theory { the Past and the Future, Mathematical and statistical developments of evolutionary theory.

Probabilities and potential, North{Holland Elsevier,

Problems and theorems in analysis,

processes,

Projective representations of the in symmetric group, Representation theory and dynamical systems

Random partitions in population genetics,

Shifted Schur functions,

Symmetric functions and Hall polynomials, 2nd edition,

The boundary of Young graph with Jack edge multiplicities,

The boundary of Young lattice and random Young tableaux, Formal power series and algebraic combinatorics

The Grothendieck group of the in symmetric group and symmetric functions with the elements of the K0-functor theory of AF-algebras, Representation of Lie groups and related

The representation of partition structures,

The representation theory of the symmetric group, Encyclopedia of mathematics and its applications 16,

The spectrum of certain invariant dierential operators associated to a Hermitian symmetric space, Lie Theory and Geometry:

The two{parameter generalization of Ewens’ random partition structure,

The two{parameter Poisson{Dirichlet distribution derived from a stable subordinator,

theorem and representations of in bisymmetric group,

Unitary representations of (G;K)-pairs connected with the in symmetric group S(1), Algebra i

Harmonic functions on multiplicative graphs and interpolation
  polynomials