Computational Methods for Matrix Groups and Group Representations

系统的对称性在数学上可以用群的概念来描述。在乘法和求逆下封闭的矩阵集是群的一个重要例子。例如，许多物理系统和其他物体的对称性是由复数上的一组矩阵捕获的。这个项目将开发必要的计算工具来构造和分析无限域上的有限矩阵群，如复数。这些方法将立即应用于许多科学和工程领域，特别是量子计算理论。

The symmetry of a system is captured mathematically by the notion of a group. A set of matrices closed under multiplication and the taking of inverses is an important example of a group. For instance, the symmetries of many physical systems and other objects are captured by a group of matrices over the complex numbers. This project will develop the computational tools necessary for constructing and analyzing finite matrix groups over infinite fields such as the complex numbers. These methods will find immediate application to many areas of science and engineering and, in particular, to the theory of quantum computation.