We describe a method to analyze and decompose the dynamics of a bilinear control system subject to symmetries. The method is based on the concept of generalized Young symmetrizers of representation theory. It naturally applies to the situation where the system evolves on a tensor product space and there exists a finite group of symmetries for the dynamics which interchanges the various factors. This is the case for quantum mechanical multipartite systems, such as spin networks, where each factor of the tensor product represents the state of one of the component systems. We present several examples of application.

中文翻译：

---

具有对称性的双线性控制系统的动态分解

我们描述了一种分析和分解受对称性影响的双线性控制系统动力学的方法。该方法基于表示理论的广义Young对称器的概念。它自然适用于系统在张量积空间上演化且存在有限的对称对称性的情况，这些对称性可以交换各种因素。对于量子机械多部分系统（例如自旋网络）就是这种情况，其中张量积的每个因数代表一个组成系统之一的状态。我们提供了几个应用示例。