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Irreducible restrictions of representations of symmetric groups in small characteristics: reduction theorems

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Abstract

We study irreducible restrictions of modules over symmetric groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. Such results are known 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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Acknowledgements

We are grateful to the anonymous referee and Gunter Malle for careful reading of the paper and multiple useful remarks.

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Authors and Affiliations

  1. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA

    Alexander Kleshchev

  2. Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, 30167, Hannover, Germany

    Lucia Morotti

  3. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Pham Huu Tiep

Authors
  1. Alexander Kleshchev
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  2. Lucia Morotti
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  3. Pham Huu Tiep
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Corresponding author

Correspondence to Alexander Kleshchev.

Additional information

The first author was supported by the NSF Grant DMS-1700905 and the DFG Mercator program through the University of Stuttgart. 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. This work was also supported by the NSF Grant DMS-1440140 and Simons Foundation while all three authors were in residence at the MSRI during the Spring 2018 semester.

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Kleshchev, A., Morotti, L. & Tiep, P.H. Irreducible restrictions of representations of symmetric groups in small characteristics: reduction theorems. Math. Z. 293, 677–723 (2019). https://doi.org/10.1007/s00209-018-2203-1

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