Categorical representations of the modular group

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...

Categorical representations of categorical groups

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A simple example is computed in explicit detail.

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).

Modular irreducible representations of the symmetric group as linear codes

We describe a particularly easy way of evaluating the modular irreducible matrix representations of the symmetric group. It shows that Specht’s approach to the ordinary irreducible representations, along Specht polynomials, can be unified with Clausen’s approach to the modular irreducible representations using symmetrized standard bideterminants. The unified method, using symmetrized Specht pol...