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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Schubert calculus and torsion explosion
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by Geordie Williamson; with a joint appendix with Alex Kontorovich; with a joint appendix with Peter J. McNamara PDF
J. Amer. Math. Soc. 30 (2017), 1023-1046 Request permission

Abstract:

The author observes that certain numbers occurring in Schubert calculus for $\text {SL}_n$ also occur as entries in intersection forms controlling decompositions of Soergel bimodules in higher rank. These numbers grow exponentially. This observation gives many counter-examples to the expected bounds in Lusztig’s conjecture on the characters of simple rational modules for $\text {SL}_n$ over fields of positive characteristic. The examples also give counter-examples to the James conjecture on decomposition numbers for symmetric groups.
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Additional Information
  • Geordie Williamson
  • Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111, Bonn, Germany
  • MR Author ID: 845262
  • Email: geordie@mpim-bonn.mpg.de
  • Alex Kontorovich
  • Affiliation: Rutgers University, New Brunswick, New Jersey
  • MR Author ID: 704943
  • ORCID: 0000-0001-7626-8319
  • Email: alex.kontorovich@rutgers.edu
  • Peter J. McNamara
  • Affiliation: University of Queensland, Brisbane, Queensland, Australia
  • MR Author ID: 791816
  • Email: p.mcnamara@uq.edu.au
  • Received by editor(s): June 22, 2015
  • Received by editor(s) in revised form: May 5, 2016, and August 4, 2016
  • Published electronically: October 20, 2016
  • Additional Notes: The first author of the Appendix is partially supported by an NSF CAREER grant DMS-1455705 and an Alfred P. Sloan Research Fellowship.

  • Dedicated: Dedicated to Meg and Gong.
  • © Copyright 2016 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 30 (2017), 1023-1046
  • MSC (2010): Primary 20C20, 20G05; Secondary 14N15, 14M15
  • DOI: https://doi.org/10.1090/jams/868
  • MathSciNet review: 3671935