## 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.

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 |

## Keywords

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