We define and investigate algebraic torus actions on quiver Grassmannians for nilpotent representations of the equioriented cycle. Examples of such varieties are type $A$ flag varieties, their linear degenerations and finite-dimensional approximations of both the affine flag variety and affine Grassmannian for ${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n$. We show that these quiver Grassmannians equipped with our specific torus action are GKM-varieties and that their moment graph admits a combinatorial description in terms of the coefficient quiver of the underlying quiver representations. By adapting to our setting results by Gonzales, we are able to prove that moment graph techniques can be applied to construct module bases for the equivariant cohomology of the quiver Grassmannians listed above.

我们定义并研究了颤动格拉斯曼函数上的代数环面作用，以获得等向环的幂零表示。此类品种的例子是类型$A$旗簇，它们的线性退化和仿射旗簇和仿射格拉斯曼的有限维近似${\mathrm{GL}<!--FUNCTION\; APPLICATION-->}_n$。我们表明，这些配备了我们特定环面动作的箭袋格拉斯曼人是 GKM 变体，并且它们的矩图允许根据基础箭袋表示的系数箭袋进行组合描述。通过适应冈萨雷斯的设置结果，我们能够证明矩图技术可以应用于构造上面列出的箭袋格拉斯曼函数的等变上同调的模基。