The Peterson variety and the wonderful compactification

Bălibanu, Ana

doi:10.1090/ert/499

The Peterson variety and the wonderful compactification
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by Ana Bălibanu

Represent. Theory 21 (2017), 132-150

DOI: https://doi.org/10.1090/ert/499

Published electronically: July 20, 2017

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Abstract:

We look at the centralizer in a semisimple algebraic group $G$ of a regular nilpotent element $e\in \text {Lie}(G)$ and show that its closure in the wonderful compactification is isomorphic to the Peterson variety. It follows that the closure in the wonderful compactification of the centralizer $G^x$ of any regular element $x\in \text {Lie}(G)$ is isomorphic to the closure of a general $G^x$-orbit in the flag variety. We also give a description of the $G^e$-orbit structure of the Peterson variety.

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