The Peterson Variety and the Wonderful Compactification
Ana Balibanu

TL;DR
This paper establishes a geometric connection between the Peterson variety and the wonderful compactification by showing the closure of a centralizer of a regular nilpotent element is isomorphic to the Peterson variety, revealing new structural insights.
Contribution
It demonstrates that the closure of the centralizer of a regular nilpotent element in the wonderful compactification is isomorphic to the Peterson variety, providing a new geometric perspective.
Findings
The closure of the centralizer of a regular nilpotent element is isomorphic to the Peterson variety.
The closure of the centralizer of any regular element is isomorphic to the closure of a general orbit in the flag variety.
The paper describes the orbit structure of the Peterson variety under the action of the centralizer.
Abstract
We look at the centralizer in a semisimple algebraic group of a regular nilpotent element, 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 of any regular element is isomorphic to the closure of a general -orbit in the flag variety. We also give a description of the -orbit structure of the Peterson variety.
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