论文标题
Askey-Wilson多项式和分支定律
Askey-Wilson Polynomials and Branching Laws
论文作者
论文摘要
特殊功能的连接系数公式描述了特殊功能形成的碱基下基矩阵的更改。这种公式与表示理论中的分支问题有关。 ASKEY-WILSON多项式是最通用的1变量特殊功能之一。我们的主要结果是用于转移非对称Askey-Wilson多项式参数之一的连接系数公式。我们还展示了如何使用其中一个结果来重新启动对称案例中Askey和Wilson的旧结果。证明方法结合了一个更简单的特殊情况，即将一个参数通过Q的因子与使用涉及的过渡矩阵的共生条件特性相结合。支持计算使用NOUMI表示形式，并基于简单公式，用于某些基本的Hecke代数元素如何作用于天然几乎对称的Laurent多项式。
Connection coefficient formulas for special functions describe change of basis matrices under a parameter change, for bases formed by the special functions. Such formulas are related to branching questions in representation theory. The Askey-Wilson polynomials are one of the most general 1-variable special functions. Our main results are connection coefficient formulas for shifting one of the parameters of the nonsymmetric Askey-Wilson polynomials. We also show how one of these results can be used to re-prove an old result of Askey and Wilson in the symmetric case. The method of proof combines establishing a simpler special case of shifting one parameter by a factor of q with using a co-cycle condition property of the transition matrices involved. Supporting computations use the Noumi representation and are based on simple formulas for how some basic Hecke algebra elements act on natural almost symmetric Laurent polynomials.
