<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Kuznetsov, V</style></author><author><style face="normal" font="default" size="100%">Mangazeev, V</style></author><author><style face="normal" font="default" size="100%">Sklyanin, Evgeni</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Q-operator and factorised separation chain for Jack polynomials</style></title><secondary-title><style face="normal" font="default" size="100%">Indagationes Mathematicae, New Series</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://arxiv.org/abs/math.CA/0306242</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">451-482</style></pages><isbn><style face="normal" font="default" size="100%">0019-3577</style></isbn><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Applying 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.
</style></abstract><custom1><style face="normal" font="default" size="100%">arXiv:math.CA/0306242</style></custom1><custom2><style face="normal" font="default" size="100%">MR2083086</style></custom2></record></records></xml>