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Generalizing Schubert cells in type A and a cell decomposition if Springerfibres in type A found by L. Fresse we prove that varieties of complete flagsin nilpotent representations of an oriented cycle admit an affine celldecomposition parametrized by multi-tableaux. We show that they carry a torusoperation and describe the T-equivariant cohomology usingGoresky-Kottwitz-MacPherson-theory. As an application of the cell decompositionwe obtain a vector space basis of certain modules (for quiver Hecke algebras ofnilpotent representations of this quiver), similar modules have been studied byKato as analogues of standard modules.

Cell decompositions of quiver flag varieties for nilpotent representations of the oriented cycle