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Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems


Authors: Alexander Kleshchev, Lucia Morotti and Pham Huu Tiep
Journal: Represent. Theory 24 (2020), 115-150
MSC (2010): Primary 20C20, 20C30, 20E28
DOI: https://doi.org/10.1090/ert/538
Published electronically: February 20, 2020
MathSciNet review: 4066477
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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 fΓΌr Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz UniversitΓ€t 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.
Article copyright: © Copyright 2020 American Mathematical Society