The indices of order 2, 4, 6 together with other higher even degree indices, as well as the anomaly numbers (the indices of degree 3), are known invariants of finite dimensional representations of simple Lie algebras. The definition and properties of such indices adapted to individual orbits of the non-crystallographic reflection groups are presented. It is shown that the representation-orbit replacement yields the following generalizations: the indices, the anomaly numbers and the embedding indices of irreducible representations become those of orbits.

中文翻译：

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非结晶型 Coxeter 群的嵌套多面体和轨道指数

2、4、6 阶指数与其他更高偶数指数以及异常数（3 阶指数）一起，是简单李代数的有限维表示的已知不变量。介绍了适用于非晶体反射群的各个轨道的此类指数的定义和性质。结果表明，表示轨道替换产生以下概括：不可约表示的索引、异常数和嵌入索引成为轨道的索引。