Adequate groups of low degree

Robert Guralnick, Florian Herzig, Pham Huu Tiep

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

The notion of adequate subgroups was introduced by Jack Thorne. It is a weakening of the notion of big subgroups used in generalizations of the Taylor–Wiles method for proving the automorphy of certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown by Guralnick, Herzig, Taylor, and Thorne that if the dimension is small compared to the characteristic, then all absolutely irreducible representations are adequate. Here we extend that result by showing that, in almost all cases, absolutely irreducible k+modules in characteristic p whose irreducible G+- summands have dimension less than p (where G+ denotes the subgroup of G generated by all p-elements of G) are adequate.

Original languageEnglish (US)
Pages (from-to)77-148
Number of pages72
JournalAlgebra and Number Theory
Volume9
Issue number1
DOIs
StatePublished - Jan 1 2015

Keywords

  • Adequate representations
  • Artin–Wedderburn theorem
  • Automorphic representations
  • Galois representations
  • Irreducible representations

ASJC Scopus subject areas

  • Algebra and Number Theory

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