Permutation actions on Quiver Grassmannians for the equioriented cycle via GKM-theory

In our previous work, we equipped quiver Grassmannians for nilpotent representations of the equioriented cycle with an action of an algebraic torus. We show here that the equivariant cohomology ring is acted upon by a product of symmetric groups and we investigate this permutation action via GKM techniques. In the case of (type A) flag varieties, or Schubert varieties therein, we recover Tymoczko's results on permutation representations.

Automated summary

This paper explores the action of an algebraic torus on the quiver Grassmannians for nilpotent representations of the equioriented cycle and discovers the permutation action of symmetric groups on the equivariant cohomology ring. The GKM techniques are used to investigate this permutation action. Specifically, the paper recovers Tymoczko's findings on permutation representations for (type A) flag varieties or Schubert varieties therein.