Adequate groups of low degree

作者：Guralnick Robert^*; Herzig Florian; Pham Huu Tiep

来源：Algebra and Number Theory, 2015, 9(1): 77-147.

DOI：10.2140/ant.2015.9.77

• Artin-Wedderburn theorem
• irreducible representations
• automorphic representations
• Galois representations
• adequate representations

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 kG-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.

• 出版日期2015