Q-operator and factorised separation chain for Jack polynomials

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JournalIndagationes Mathematicae
DatePublished - 15 Dec 2003
Issue number3-4
Volume14
Number of pages32
Pages (from-to)451-482
Original languageEnglish

Abstract

Applying Baxter's method of the Q-operator to the set of Sekiguchi's commuting partial differential operators we show that Jack polynomials P-lambda((1/g))(x(1,...,)x(n)) are eigenfunctions of a one-parameter family of integral operators Q(z). The operators Q(z) are expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Q(zk) we construct an integral operator S,, factorising Jack polynomials into products of hypergeometric polynomials of one variable. The operator S-n admits a factorisation described in terms of restricted Jack polynomials P-lambda((1/g))(x(1,...,)x(k), 1,...,1). Using the operator Q(z) for z = O we give a simple derivation of a previously known integral representation for Jack polynomials.

    Research areas

  • Jack polynomials, integral operators, SYMMETRIC FUNCTIONS, SINGULAR VECTORS, TODA CHAIN, VARIABLES, SYSTEM, MODEL, ALGEBRA

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