publication . Preprint . Article . 2020

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

Alexander Kleshchev; Lucia Morotti; Pham Huu Tiep;
Open Access English
  • Published: 20 Feb 2020
Abstract
We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is 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. In view of our earlier work on symmetric groups we may consider only the restriction of irreducible modules over alternating groups which do not extend to symmetric groups. This work fits into the Aschbacher-Scott program on maximal subgroups of finite classical groups.
Subjects
arXiv: Mathematics::Group Theory
free text keywords: Mathematics - Representation Theory, Mathematics - Group Theory, Mathematics (miscellaneous), Mathematics, Algebra
Funded by
NSF| Monoidal Categories and Categorification in Classical Representation Theory
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1700905
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Mathematical Sciences Research Institute (MSRI)
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1440140
,
NSF| Group Representations and Applications
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 1840702
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
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publication . Preprint . Article . 2020

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

Alexander Kleshchev; Lucia Morotti; Pham Huu Tiep;