## 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.## References

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## Bibliographic Information

**Ana Bălibanu**- Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637
- Email: ana@math.uchicago.edu
- Received by editor(s): May 30, 2016
- Received by editor(s) in revised form: February 23, 2017
- Published electronically: July 20, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Represent. Theory
**21**(2017), 132-150 - MSC (2010): Primary 20G05
- DOI: https://doi.org/10.1090/ert/499
- MathSciNet review: 3673527