The 7-modular representations of Janko's smallest simple group

Asymptotic Results on Modular Representations of Symmetric Groups and Almost Simple Modular Group Algebras

In fact, this is a question about infinite simple groups because it is easy for G finite, and because a non-trivial normal subgroup gives rise to a non-trivial ideal different from the augmentation ideal. Also note that the problem reduces easily to the question on when the augmentation ideal is simple as a ring. The first interesting class of groups with almost simple FG was discovered in [3]....

Modular Representations of Simple Lie Algebras

In spite of many efforts over the past 50 years, the irreducible representations of the Lie algebra of a simple algebraic group over a field of prime characteristic are poorly understood. Recent work on quantum groups at a root of unity has provided new impetus for the subject. This article surveys what has been done and what remains to be done.

Deformation of Outer Representations of Galois Group

To a hyperbolic smooth curve defined over a number-field one naturally associates an "anabelian" representation of the absolute Galois group of the base field landing in outer automorphism group of the algebraic fundamental group. In this paper, we introduce several deformation problems for Lie-algebra versions of the above representation and show that, this way we get a richer structure than t...

On the Modular Representations of the Symmetric Group (III).

In a previous paper2 the author commented upon an idea of D. E. Littlewood' for defining the indecomposables of the regular representation of Sn, and showed how it could be utilized to characterize the modular irreducible components. A modification of Littlewood's idea is presented here which throws new light upon the whole problem. Young's rule3 for constructing the "seminormal" representation...

On the Modular Representations of the Symmetric Group (II).