代数$\mathfrak{gl}_3$和超几何函数的Clebsh-Gordan系数
Clebsh-Gordan coefficients for the algebra $\mathfrak{gl}_3$ and hypergeometric functions
摘要：
计算了李代数$\mathfrak{gl}_3$在Gelfand-Tsetlin基上的Clebsh-Gordan系数.与以前的论文相比，结果是作为一个明确的公式。为了获得结果，使用在群$GL_3$上的函数空间中的表示的实现。允许进行Clebsh-Gordan系数计算的关键事实是这样一个定理，即对应于Gelfand-Tsetlin基向量的函数可以通过广义超几何函数表示。
英文摘要：
The Clebsh-Gordan coefficients for the Lie algebra $\mathfrak{gl}_3$ in the Gelfand-Tsetlin base are calculated. In contrast to previous papers the result is given as an explicit formula. To obtain the result a realization of a representation in the space of functions on the group $GL_3$ is used. The keystone fact that allows to carry the calculation of Clebsh-Gordan coefficients is the theorem that says that functions corresponding to Gelfand-Tsetlin base vectors can be expressed through generalized hypergeometric functions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
