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

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Abstract
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.
Funding Information
  • PRIN2017 (CUP E8419000480006, CUP E8419000480006)
  • MIUR Excellence Department Project (CUP E83C18000100006, CUP E83C18000100006)

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