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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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Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems
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by Alexander Kleshchev, Lucia Morotti and Pham Huu Tiep PDF
Represent. Theory 24 (2020), 115-150 Request permission

Abstract:

We study irreducible restrictions from modules over alternating groups to proper subgroups, and prove reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This problem had been solved when the characteristic of the ground field is greater than $3$, but the small characteristics cases require a substantially more delicate analysis and new ideas. This work fits into the Aschbacher-Scott program on maximal subgroups of finite classical groups.
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Additional Information
  • Alexander Kleshchev
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • MR Author ID: 268538
  • Email: klesh@uoregon.edu
  • Lucia Morotti
  • Affiliation: Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, 30167 Hannover, Germany
  • MR Author ID: 1037296
  • Email: morotti@math.uni-hannover.de
  • Pham Huu Tiep
  • Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
  • MR Author ID: 230310
  • Email: tiep@math.rutgers.edu
  • Received by editor(s): September 25, 2019
  • Received by editor(s) in revised form: January 10, 2020
  • Published electronically: February 20, 2020
  • Additional Notes: The first author was supported by the NSF grant DMS-1700905 and the DFG Mercator program through the University of Stuttgart.
    This work was also supported by the NSF grant DMS-1440140 and the Simons Foundation while all three authors were in residence at the MSRI during the Spring 2018 semester.
    The second author was supported by the DFG grant MO 3377/1-1, and the DFG Mercator program through the University of Stuttgart.
    The third author was supported by the NSF grants DMS-1839351 and DMS-1840702, and the Joshua Barlaz Chair in Mathematics.
  • © Copyright 2020 American Mathematical Society
  • Journal: Represent. Theory 24 (2020), 115-150
  • MSC (2010): Primary 20C20, 20C30, 20E28
  • DOI: https://doi.org/10.1090/ert/538
  • MathSciNet review: 4066477