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.
Lanini, M., Putz, A. (2023). Permutation actions on Quiver Grassmannians for the equioriented cycle via GKM-theory. JOURNAL OF ALGEBRAIC COMBINATORICS, 57(3), 915-956 [10.1007/s10801-022-01211-5].
Permutation actions on Quiver Grassmannians for the equioriented cycle via GKM-theory
Lanini M.;
2023-01-01
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.| File | Dimensione | Formato | |
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