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Q-operator and factorised separation chain for Jack polynomials

TitleQ-operator and factorised separation chain for Jack polynomials
Publication TypeJournal Article
Year of Publication2003
AuthorsKuznetsov V, Mangazeev V, Sklyanin E
JournalIndagationes Mathematicae, New Series
Volume14
Pagination451-482
AbstractApplying Baxter's method of the Q-operator to the set of Sekiguchi's commuting partial differential operators we show that Jack polynomials P(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_{z_k} we construct an integral operator S_n 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(x_1,...,x_k,1,...,1). Using the operator Q_z for z=0 we give a simple derivation of a previously known integral representation for Jack polynomials.
URLhttp://arxiv.org/abs/math.CA/0306242
E-print numberarXiv:math.CA/0306242
MathRevMR2083086

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