Non-linear Sylow branching coefficients for symmetric groups

On Decomposition Numbers and Branching Coefficients for Symmetric and Special Linear Groups

Introduction In 13] { 15] we have obtained results generalizing the classical Branching Theorem for symmetric groups to the case of modular representations. For example we have described the socle of the restriction, D # n?1 , of an arbitrary (modular) irreducible representation D of the symmetric group n to the natural subgroup n?1. In particular, it turns out that this socle is always multipl...

The Sylow Subgroups of the Symmetric Groups

The aim of this paper is to give a direct approach to the study of the Sylow ^-subgroups Sn of the symmetric group of degree pn. [We assume throughout that p^2.] Many of the results are already known and are treated in a paper by Kaloujnine where he uses a particular representation by means of "reduced polynomials."1 It has seemed worth while to restate some of his results using the concept of ...

Quantization of branching coefficients for classical Lie groups

We study natural quantizations of branching coefficients corresponding to the restrictions of the classical Lie groups to their Levi subgroups. We show that they admit a stable limit which can be regarded as a q-analogue of a tensor product multiplicity. According to a conjecture by Shimozono, the stable one-dimensional sum for nonexceptional affine crystals are expected to occur as special cas...

Branching Rules for Modular Representations of Symmetric Groups, Iv

Sylow Groups of Groups of Polynomial Permutations

We enumerate and describe the Sylow p-groups of the group of polynomial permutations of the integers mod p . MSC 2000: primary 20D20, secondary 11T06, 13M10, 11C08, 13F20, 20E18.