A root system is splint if it is a decomposition into a union of two disjoint root systems. Examples of such root systems arise naturally in studying embeddings of reductive Lie subalgebras into simple Lie algebras. Given a splint root system, one can try to understand its branching rule. In this paper we discuss methods to understand such branching rules, and give precise formulas for specific cases, including the restriction functor from the exceptional Lie algebra \(\mathfrak {g}_{2}\) to \(\mathfrak {sl}_{3}\).

中文翻译：

---

夹板根系统的分支规则

如果根系统分解为两个不相交的根系统的并集，则该根系统是夹板的。在研究将还原李子代数嵌入到简单李代数中时，自然会出现这种根系统的例子。给定夹板根系统，可以尝试了解其分支规则。在本文中，我们讨论了理解此类分支规则的方法，并针对特定情况给出了精确的公式，包括从特殊的李代数\（\ mathfrak {g} _ {2} \）到\（\ mathfrak {sl}的限制函子。_ {3} \）。