Q-operator and factorised separation chain for Jack polynomials
Q-operator and factorised separation chain for Jack polynomials
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Jack 多项式的 Q 算子和因式分解分离链
DOI：
10.1016/s0019-3577(03)90057-7
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
E. Sklyanin
中科院分区：
文献类型：
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作者：
V. Kuznetsov;V. Mangazeev;E. Sklyanin
将q算子的Baxter方法应用于Sekiguchi可交换偏微分算子集合，证明了Jack多项式Pλ（1/g)（χ1，…，χn）…，χn）是单参数积分算子族Qz的特征函数。算符qzr用Dirichlet-Liouville n维积分表示。从n个算子的复合构造了一个积分算子，它可以将j多项式分解为单变量超几何多项式的积。算子sn允许用受限杰克多项式Pλ(1/g)（x1，…，xk, 1，…1）来描述因式分解。对于z = 0，使用qz算子，我们给出了先前已知的杰克多项式的积分表示的简单推导。
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)(χ1, …, χn) …, χn) are eigenfunctions of a one-parameter family of integral operators Qz. The operators Qzare expressed in terms of the Dirichlet-Liouville n-dimensional beta integral. From a composition of n operators Qzkwe construct an integral operator Snfactorising Jack polynomials into products of hypergeometric polynomials of one variable. The operator Snadmits a factorisation described in terms of restricted Jack polynomials Pλ(1/g)(x1, …, xk, 1, … 1). Using the operator Qzfor z = 0 we give a simple derivation of a previously known integral representation for Jack polynomials.