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The (cyclic) enhanced nilpotent cone via quiver representations

An Erratum to this article was published on 09 February 2019

This article has been updated


The \({{\,\mathrm{GL}\,}}(V)\)-orbits in the enhanced nilpotent cone \(V\times \mathcal {N}\) are (essentially) in bijection with the orbits of a certain parabolic \(P\subseteq {{\,\mathrm{GL}\,}}(V)\) (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.

Change history

  • 09 February 2019

    The article “The (cyclic) enhanced nilpotent cone via quiver representations”, written by Gwyn Bellamy Magdalena Boos, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on December 17, 2018, without open access.


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The authors would like to thank C. Johnson for his very precise and valuable ideas regarding the translation between our parametrization and his original parametrization of orbits. We also thank K. Bongartz and M. Reineke for helpful remarks on the subject. The first author was partially supported by EPSRC Grant EP/N005058/1.

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Correspondence to Magdalena Boos.

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Bellamy, G., Boos, M. The (cyclic) enhanced nilpotent cone via quiver representations. manuscripta math. 161, 333–362 (2020).

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Mathematics Subject Classification

  • Primary 16G20
  • Secondary 16G60
  • 17B08