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The Peterson variety and the wonderful compactification


Author: Ana Bălibanu
Journal: Represent. Theory 21 (2017), 132-150
MSC (2010): Primary 20G05
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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Additional Information

Ana Bălibanu
Affiliation: Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL 60637
Email: ana@math.uchicago.edu

DOI: https://doi.org/10.1090/ert/499
Received by editor(s): May 30, 2016
Received by editor(s) in revised form: February 23, 2017
Published electronically: July 20, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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