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

Julia Sauter

Published 2015-09-26Version 1

Generalizing Schubert cells in type $A$ and a cell decomposition if Springer fibres in type $A$ found by L. Fresse we prove that varieties of complete flags in nilpotent representations of an oriented cycle admit an affine cell decomposition parametrized by multi-tableaux. We show that they carry a torus operation and describe the $T$-equivariant cohomology using Goresky-Kottwitz-MacPherson-theory. As an application of the cell decomposition we obtain a vector space basis of standard modules (for quiver Hecke algebras of nilpotent representations of this quiver) introduced by Kato.