Cell Decompositions of Quiver Flag Varieties for Nilpotent Representations of the Cyclic Quiver

Generalizing Schubert cells in type A and a cell decomposition of Springer fibres in type A found by L. Fresse we prove that varieties of complete flags in nilpotent representations of a cyclic quiver admit an affine cell decomposition parametrized by multi-tableaux. We show that they carry a torus operation with finitely many fixpoints. As an application of the cell decomposition we obtain a vector space basis of certain modules (for quiver Hecke algebras of nilpotent representations of this quiver), similar modules have been studied by Kato as analogues of standard modules.