3F ~ 2（1）超几何函数与二次R-矩阵代数
3F2(1) hypergeometric function and quadratic R-matrix algebra
摘要：
我们构造了一类由带谱参数的反射方程给出的二次$R$ -矩阵代数$$ R{\,}(u-v)\,T^{(1)}(u)\,R{\,}(u+v)\,T^{(2)}(v)= T^{(2)}(v)\,R{\,}(u+v)\,T^{(1)}(u)\,R{\,}(u-v), $$用某些普通的差分算子表示.这些算子在${}_3F{}_2(1)$超几何函数及其极限情形和经典的正交多项式上充当参数移位算子。将讨论与因子分解方法的关系。
英文摘要：
We construct a class of representations of the quadratic $R$-matrix algebra given by the reflection equation with the spectral parameter, $$ R{\,}(u-v)\,T^{(1)}(u)\,R{\,}(u+v)\,T^{(2)}(v)= T^{(2)}(v)\,R{\,}(u+v)\,T^{(1)}(u)\,R{\,}(u-v), $$ in terms of certain ordinary difference operators. These operators turn out to act as parameter shifting operators on the ${}_3F{}_2(1)$ hypergeometric function and its limit cases and on classical orthogonal polynomials. The relationship with the factorisation method will be discussed.
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