On extensions and branching rules for modules close to completely splittable

On extensions and branching rules for modules close to completely splittable

We describe the modules Dλ↓Σn−1 and D λ↑n+1 for certain simple KΣn-modules (completely splittable and some close to) D, where K is a field of characteristic p > 0 and Σn is the symmetric group of degree n. This result is based on an upper bound of the dimensions of the Ext-spaces between some simple modules.

On some extensions of p-restricted completely splittable GL(n)-modules

In this paper, we calculate the space ExtGL(n)(Ln(λ), Ln(μ)), where GL(n) is the general linear group of degree n over an algebraically closed field of positive characteristic, Ln(λ) and Ln(μ) are rational irreducible GL(n)-modules with highest weights λ and μ respectively, the restriction of Ln(λ) to any Levi subgroup of GL(n) is semisimple, λ is a p-restricted weight and μ does not strictly d...

Specht Modules and Branching Rules for Ariki-koike Algebras

Specht modules for an Ariki-Koike algebra Hm have been investigated recently in the context of cellular algebras (see, e.g., [GL] and [DJM]). Thus, these modules are defined as quotient modules of certain “permutation” modules, that is, defined as “cell modules” via cellular bases. So cellular bases play a decisive rôle in these work. However, the classical theory [C] or the work in the case wh...

Completely Splittable Representations of Symmetric Groups

Extensions of Baer and quasi-Baer modules