Final Activity Report Summary - REPTHOX (Representation Theory of Schur algebras)
This project studies algebraic structures arising from symmetries by their actions on spaces. One such algebraic structure of particular importance is the general linear group, the group of all invertible transformations of a space which fixes the origin. In this project, the representation theory of general linear group was studied. This is encoded in so-called Schur algebras.
For the general linear group of a two-dimensional space, the participants have explicitly described all Schur algebras in a way that gives combinatorial access to the most important (namely projective) representations by exhibiting higher symmetries. They have furthermore, for general linear groups of a space of arbitrary dimension, given an algorithm for computing the objects of another important subclass of representations - the so-called standard filtered modules. Various other results investigating certain invariants of Schur algebras and related algebras add to the improved understanding of these fundamentally important groups.
For the general linear group of a two-dimensional space, the participants have explicitly described all Schur algebras in a way that gives combinatorial access to the most important (namely projective) representations by exhibiting higher symmetries. They have furthermore, for general linear groups of a space of arbitrary dimension, given an algorithm for computing the objects of another important subclass of representations - the so-called standard filtered modules. Various other results investigating certain invariants of Schur algebras and related algebras add to the improved understanding of these fundamentally important groups.