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

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 Symmetric Groups

Over the last few weeks, we have seen lots of things in representation theory—we began by looking at an onslaught of examples to see explicitly what representations look like, we discussed character theory and looked at character tables, we talked about representations from a module-theoretic perspective, and then we saw how we can model the representation theory of the symmetric group via the ...

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.

Symmetric Units in Modular Group Algebras

Let p be a prime, G a locally finite p -group, K a commutative ring of characteristic p . The anti-automorphism g 7→ g of G extends linearly to an anti-automorphism a 7→ a∗ of KG . An element a of KG is called symmetric if a∗ = a . In this paper we answer the question: for which G and K do the symmetric units of KG form a multiplicative group. Let G be a group, K a commutative ring (with 1), an...

On Tensor Products of Modular Representations of Symmetric Groups