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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 null-cone and cohomology of vector bundles on flag varieties
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by Kari Vilonen and Ting Xue PDF
Represent. Theory 20 (2016), 482-498 Request permission

Abstract:

We study the null-cone of a semi-simple algebraic group acting on a number of copies of its Lie algebra via the diagonal adjoint action. We show that the null-cone has rational singularities in the case of $SL_3$. We observe by example that the null-cone is not normal in general and that the normalization of the null-cone does not have rational singularities in general. This is achieved by computing cohomology of certain vector bundles on flag varieties.
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Additional Information
  • Kari Vilonen
  • Affiliation: School of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia – and – Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
  • MR Author ID: 178620
  • Email: kari.vilonen@unimelb.edu.au, kari.vilonen@helsinki.fi
  • Ting Xue
  • Affiliation: School of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia – and – Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
  • MR Author ID: 779365
  • Email: ting.xue@unimelb.edu.au
  • Received by editor(s): February 3, 2016
  • Received by editor(s) in revised form: March 10, 2016, and October 14, 2016
  • Published electronically: December 23, 2016
  • Additional Notes: The first author was supported in part by NSF grants DMS-1402928 and DMS-1069316, the Academy of Finland, and the ARC grant DP150103525.
    The second author was supported in part by the ARC grants DP150103525, DE160100975, and the Academy of Finland.
  • © Copyright 2016 American Mathematical Society
  • Journal: Represent. Theory 20 (2016), 482-498
  • MSC (2010): Primary 14L99, 20G99
  • DOI: https://doi.org/10.1090/ert/491
  • MathSciNet review: 3589334