标题： 差异分割：经典不变量理论中雷诺兹算子的计算 显示英文标题

标题： Splitting the difference: Computations of the Reynolds operator in classical invariant theory

摘要： 如果$G$是一个线性约化群，并在多项式环$S$上有理地作用，那么包含$S^{G} \hookrightarrow S$具有一个唯一的$G$-等变分裂，称为雷诺兹算子。我们描述了计算魏尔著作中经典作用的雷诺兹算子的算法。这些群是一般线性群、特殊线性群、正交群和辛群，它们的经典表示为标准表示和对偶表示的直和。 显示英文摘要

摘要： If $G$ is a linearly reductive group acting rationally on a polynomial ring $S$, then the inclusion $S^{G} \hookrightarrow S$ possesses a unique $G$-equivariant splitting, called the Reynolds operator. We describe algorithms for computing the Reynolds operator for the classical actions as in Weyl's book. The groups are the general linear group, the special linear group, the orthogonal group, and the symplectic group, with their classical representations: direct sums of copies of the standard representation and copies of the dual representation.