Abstract
The {{,mathrm{GL},}}(V)-orbits in the enhanced nilpotent cone Vtimes mathcal {N} are (essentially) in bijection with the orbits of a certain parabolic Psubseteq {{,mathrm{GL},}}(V) (the mirabolic subgroup) in the nilpotent cone mathcal {N}. We give a new parameterization of the orbits in the enhanced nilpotent cone, in terms of representations of the underlying quiver. This parameterization generalizes naturally to the enhanced cyclic nilpotent cone. Our parameterizations are different from the previous ones that have appeared in the literature. Explicit translations between the different parametrizations are given.
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