## 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_{λ}^{(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_{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_{λ}^{(1/g)} (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.

Original language | English |
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Pages (from-to) | 451-482 |

Number of pages | 32 |

Journal | Indagationes Mathematicae |

Volume | 14 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 15 Dec 2003 |