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arXiv · 1609.04525

The (cyclic) enhanced nilpotent cone via quiver representations

Gwyn Bellamy·Magdalena Boos
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Abstract

The $\mathrm{GL}(V)$-orbits in the enhanced nilpotent cone $V\times\mathcal{N}(V)$ are (essentially) in bijection with the orbits of a certain parabolic $P\subseteq\mathrm{GL}(V)$ (the mirabolic subgroup) in the nilpotent cone $\mathcal{N}(V)$. 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 to the previous ones that have appeared in the literature. Explicit translations between the different parametrizations are given.

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Gwyn Bellamy, Magdalena Boos. 2016-09-15. The (cyclic) enhanced nilpotent cone via quiver representations. https://arxiv.org/abs/1609.04525

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