Let X be a complete toric variety equipped with the action of a torus T, and G a reductive algebraic group, defined over an algebraically closed field K. We introduce the notion of a compatible ∑-filtered algebra associated to X, generalizing the notion of a compatible ∑-filtered vector space due to Klyachko, where ∑ denotes the fan of X. We combine Klyachko's classification of T-equivariant vector bundles on X with Nori's Tannakian approach to principal G-bundles, to give an equivalence of categories between T-equivariant principal G-bundles on X and certain compatible ∑-filtered algebras associated to X, when the characteristic of K is 0.

令X是配备环面T的作用的完整复曲面变体，G是定义在代数闭合域K上的归约代数群。我们引入了与X相关的兼容∑滤波代数的概念，归纳了由于Klyachko而产生的兼容∑滤波向量空间的概念，其中∑表示X的扇形。我们结合的Klyachko的分类Ť上-equivariant矢量束X与诺里的Tannakian方法主要ģ -bundles，得到之间类别的一个等价Ť -equivariant主要ģ -bundles上当K的特征为0时，X和与X相关的某些兼容∑滤波的代数。