Clebsh–Gordan coefficients for the algebra 𝔤𝔩₃ and hypergeometric functions

IF 0.7 4区 数学 Q2 MATHEMATICS
D. Artamonov
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引用次数: 6

Abstract

The Clebsh–Gordan coefficients for the Lie algebra g l 3 \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 G L 3 GL_3 is used. The keystone fact that allows one to carry the calculation of Clebsh–Gordan coefficients is the theorem that says that functions corresponding to the Gelfand–Tsetlin base vectors can be expressed in terms of generalized hypergeometric functions.
代数𝔩₃和超几何函数的Clebsh-Gordan系数
李代数gl3\mathfrak的Clebsh–Gordan系数{gl}_3计算了Gelfand–Tsetlin基中的。与以前的论文相比,结果是作为一个显式公式给出的。为了得到这一结果,使用了在群GL_3上函数空间中的一个表示的实现。允许计算Clebsh–Gordan系数的关键事实是定理,该定理表明,与Gelfand–Tsetlin基向量对应的函数可以用广义超几何函数表示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.00
自引率
12.50%
发文量
52
审稿时长
>12 weeks
期刊介绍: This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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