## Details

Original language | English |
---|---|

Pages (from-to) | 115-150 |

Number of pages | 36 |

Journal | Representation Theory of the American Mathematical Society |

Volume | 24 |

Issue number | 4 |

Publication status | Published - 20 Feb 2020 |

## 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.

## ASJC Scopus subject areas

- Mathematics(all)
**Mathematics (miscellaneous)**

## Cite this

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**Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems.**/ Kleshchev, Alexander; Morotti, Lucia; Tiep, Pham.

In: Representation Theory of the American Mathematical Society, Vol. 24, No. 4, 20.02.2020, p. 115-150.

Research output: Contribution to journal › Article › Research › peer review

*Representation Theory of the American Mathematical Society*, vol. 24, no. 4, pp. 115-150. https://doi.org/10.1090/ERT/538

*Representation Theory of the American Mathematical Society*,

*24*(4), 115-150. https://doi.org/10.1090/ERT/538

}

TY - JOUR

T1 - Irreducible restrictions of representations of alternating groups in small characteristics: Reduction theorems

AU - Kleshchev, Alexander

AU - Morotti, Lucia

AU - Tiep, Pham

N1 - Funding Information: Received by the editors September 25, 2019, and, in revised form, January 10, 2020. 2010 Mathematics Subject Classification. Primary 20C20, 20C30, 20E28. 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.

PY - 2020/2/20

Y1 - 2020/2/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85084409052&partnerID=8YFLogxK

U2 - 10.1090/ERT/538

DO - 10.1090/ERT/538

M3 - Article

VL - 24

SP - 115

EP - 150

JO - Representation Theory of the American Mathematical Society

JF - Representation Theory of the American Mathematical Society

SN - 1088-4165

IS - 4

ER -