标题： 从特殊函数的角度看量子代数$su_q(1,1)$ 显示英文标题

标题： On the quantum algebra $su_q(1,1)$ from a Special Function standpoint

摘要： 在本文中，我们研究两个酉不可约表示的张量积，以及一个酉不可约表示与有限维表示的张量积，并确定相应的克莱布施-戈登系数。 使用冯·诺伊曼的投影算子方法，我们得到了这些系数的显式表示，这使我们能够将它们表示为对称的q-超几何级数。 最后，通过利用q-超几何函数的性质，我们以统一且直接的方式推导出克莱布施-戈登系数的若干性质，包括一些新的结果。 显示英文摘要

摘要： In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan coefficients. Using von Neumann's projection operator method, we obtain an explicit representation of these coefficients, which allows us to express them as symmetric q-hypergeometric series. Finally, by leveraging the properties of the q-hypergeometric function, we derive several properties of the Clebsch-Gordan coefficients, including a number of new results, in a unified and straightforward manner.