Symmetric weights and $s$-representations

Representations of symmetric groups

In this thesis we study the ordinary and the modular representation theory of the symmetric group. In particular we focus our work on different important open questions in the area. 1. Foulkes’ Conjecture In Chapter 2 we focus our attention on the long standing open problem known as Foulkes’ Conjecture. We use methods from character theory of symmetric groups to determine new information on the...

Representations of Symmetric Groups

A surprising theorem in the modular representation theory of symmetric groups uses induction and restriction functors to define an action of an affine Kac-Moody special linear algebra on the level of Grothendieck groups. This action identifies the direct sum of Grothendieck groups with an integrable highest weight module of the Kac-Moody algebra. The purpose of this write-up is to provide a gen...

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

The symmetric group - representations, combinatorial algorithms, and symmetric functions

Characterization and Properties of (R, S)-Symmetric, (R, S)-Skew Symmetric, and (R, S)-Conjugate Matrices

SIAM J. Matrix Anal Appl. 26 (2005) 748–757 Abstract. Let R ∈ C and S ∈ C be nontrivial involutions; i.e., R = R 6= ±Im and S = S 6= ±In. We say that A ∈ C is (R,S)-symmetric ((R,S)-skew symmetric) if RAS = A (RAS = −A). We give an explicit representation of an arbitrary (R,S)-symmetric matrix A in terms of matrices P andQ associatedwith R and U and V associatedwith S. If R = R, then the least ...