多变量Rachah-Wilson多项式的双谱性
Bispectrality of multivariable Racah-Wilson polynomials
摘要：
我们构造了R^p中差分算子的交换代数Ax，它依赖于由Tratnik [27]考虑的多变量Racah多项式R_p（n;x）对角化的p+3个实参数.对于变量x=（x_1，x_2，...，x_p）之间存在一个隐藏的对偶。解析延拓允许我们构造另一个交换代数变量n=（n_1，n_2，.，n_p），它也被R_p（n;x）对角化。因此R_p（n;x）在Duistermaat和Grunbaum [8]意义下解决了一个多变量离散双谱问题。由于Racah多项式中变量和参数的变化给出了多元Wilson多项式[26]，因此A_x和A_n中变量和参数的这种变化导致了多元Wilson多项式的双谱交换代数。
英文摘要：
We construct a commutative algebra A_x of difference operators in R^p, depending on p+3 real parameters which is diagonalized by the multivariable Racah polynomials R_p(n;x) considered by Tratnik [27]. It is shown that for specific values of the variables x=(x_1,x_2,...,x_p) there is a hidden duality between n and x. Analytic continuation allows us to construct another commutative algebra A_n in the variables n=(n_1,n_2,...,n_p) which is also diagonalized by R_p(n;x). Thus R_p(n;x) solve a multivariable discrete bispectral problem in the sense of Duistermaat and Grunbaum [8]. Since a change of the variables and the parameters in the Racah polynomials gives the multivariable Wilson polynomials [26], this change of variables and parameters in A_x and A_n leads to bispectral commutative algebras for the multivariable Wilson polynomials.
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