标题： 李代数 so(5) = sp(2), su(3), 和 g(2) 的图形张量积约化方案 显示英文标题

标题： Graphical Tensor Product Reduction Scheme for the Lie Algebras so(5) = sp(2), su(3), and g(2)

摘要： 我们详细开发了一种图形张量积约化方案，该方案最初由Antoine和Speiser提出，适用于简单的秩2李代数so(5)=sp(2)、su(3)和g(2)。 这导致了一种高效的实际方法，将不可约表示的张量积约化为这些表示的和。 为此，给定表示的二维权图被放置在一个不可约表示的“景观”中。 我们为这三个简单秩2李代数提供了大量表示的景观和权图。 我们还应用了代数“腰带”方法，该方法对于中等大小的表示的手动计算效率较低。 基于图形方法的张量积约化计算机代码也已开发完成，并可根据要求从作者处获得。 显示英文摘要

摘要： We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2), su(3), and g(2). This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a "landscape" of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic "girdle" method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.