Adequate subgroups and indecomposable modules
| Autor: | Pham Huu Tiep, Robert M. Guralnick, Florian Herzig |
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| Rok vydání: | 2017 |
| Předmět: |
Classical group
Pure mathematics Artin–Wedderburn theorem Absolutely irreducible General Mathematics Dimension (graph theory) Automorphic form Group Theory (math.GR) 01 natural sciences 0103 physical sciences FOS: Mathematics Number Theory (math.NT) Representation Theory (math.RT) 0101 mathematics Mathematics Mathematics - Number Theory Applied Mathematics 010102 general mathematics 16. Peace & justice Galois module Field of definition 010307 mathematical physics 20C20 11F80 Indecomposable module Mathematics - Group Theory Mathematics - Representation Theory |
| Zdroj: | Journal of the European Mathematical Society. 19:1231-1291 |
| ISSN: | 1435-9855 |
| DOI: | 10.4171/jems/692 |
| Popis: | The notion of adequate subgroups was introduced by Jack Thorne [59]. It is a weakening of the notion of big subgroups used by Wiles and Taylor in proving automorphy lifting theorems for certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown in [22] and [23] that if the dimension is smaller than the characteristic then almost all absolutely irreducible representations are adequate. We extend the results by considering all absolutely irreducible modules in characteristic p of dimension p. This relies on a modified definition of adequacy, provided by Thorne in [60], which allows p to divide the dimension of the module. We prove adequacy for almost all irreducible representations of SL_2(p^a) in the natural characteristic and for finite groups of Lie type as long as the field of definition is sufficiently large. We also essentially classify indecomposable modules in characteristic p of dimension less than 2p-2 and answer a question of Serre concerning complete reducibility of subgroups in classical groups of low dimension. Comment: Final version. 58 pages |
| Databáze: | OpenAIRE |
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