半单李代数的仿射扩张分支规则
Branching rules of semi-simple Lie algebras using affine extensions
摘要：
给出了两个有限维半单李代数的嵌入p在g中的分支系数的一个封闭公式。该公式是基于无扭仿射扩展的p.它导致了一个简单的算法的分支规则的计算，这是一个模拟的拉卡-Speiser算法的张量积的替代证明。我们提出了一些简单的应用程序，并描述如何积分表示分支系数可以获得。在最后一部分中，我们评论了我们的方法与手征代数g_k的WZW模型的熔合环的NIM-表示理论的关系。事实上，对于这些模型，每个在g中嵌入p都会导致k级的NIM-rep无穷大。在这些NIM代表可以扩展到有限水平的情况下，我们得到了一个类似Verlinder的分支系数公式。
英文摘要：
We present a closed formula for the branching coefficients of an embedding p in g of two finite-dimensional semi-simple Lie algebras. The formula is based on the untwisted affine extension of p. It leads to an alternative proof of a simple algorithm for the computation of branching rules which is an analog of the Racah-Speiser algorithm for tensor products. We present some simple applications and describe how integral representations for branching coefficients can be obtained. In the last part we comment on the relation of our approach to the theory of NIM-reps of the fusion rings of WZW models with chiral algebra g_k. In fact, it turns out that for these models each embedding p in g induces a NIM-rep at level k to infinity. In cases where these NIM-reps can be be extended to finite level, we obtain a Verlinde-like formula for branching coefficients.
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