Enhanced nilpotent representations of a cyclic quiver

We de ne a set of \enhanced" nilpotent quiver representations that generalizes both the enhanced nilpotent cone and the colored nilpotent cone. This set admits an action by an associated algebraic group K with nitely many orbits. We de ne a combinatorial set that parametrizes the set of orbits under this action and we derive a purely combinatorial formula for the dimension of an orbit. Finally, we present a conjectural combinatorial description of the closure order.