Irreducible restrictions of representations of symmetric and alternating groups in small characteristics

Alexander Kleshchev, Lucia Morotti, Pham Huu Tiep

Research output: Contribution to journalArticlepeer-review

Abstract

Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such a classification 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. Our results fit into the Aschbacher-Scott program on maximal subgroups of finite classical groups.

Original languageEnglish (US)
Article number107184
JournalAdvances in Mathematics
Volume369
DOIs
StatePublished - Aug 5 2020
Externally publishedYes

Keywords

  • Alternating groups
  • Irreducible restrictions
  • Modular representations
  • Symmetric groups

ASJC Scopus subject areas

  • Mathematics(all)

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