Q-operator and factorised separation chain for Jack polynomials

Vadim B. Kuznetsov*, Vladimir V. Mangazeev, Evgeny K. Sklyanin

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    35 Citations (Scopus)


    Applying Baxter's method of the Q-operator to the set of Sekiguchi's commuting partial differential operators we show that Jack polynomials Pλ(1/g) (x1, ...,xn) are eigenfunctions of a one-parameter family of integral operators Qz. The operators Qz are expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Qzk we construct an integral operator Sn factorising Jack polynomials into products of hypergeometric polynomials of one variable. The operator Sn admits a factorisation described in terms of restricted Jack polynomials Pλ(1/g) (x1, ...,xk, 1, ..., 1). Using the operator Qz for z = 0 we give a simple derivation of a previously known integral representation for Jack polynomials.

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


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