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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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The Peterson variety and the wonderful compactification
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by Ana Bălibanu PDF
Represent. Theory 21 (2017), 132-150 Request permission

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
  • 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