New types of infinite-dimensional representations of symmetry algebras have started to appear in conformal field theory and non hermitian quantum. This project aims to classify indecomposable representations beyond the so-called category O, by developing systematic approaches to differential operator realisations. This will involve generalisations of the familiar and ubiquitous hypergeometric functions. It will also facilitate the introduction of new exactly solvable models in statistical physics and quantum mechanics.

Project members

Supervisor: Ian Marquette

Dr Ian Marquette

ARC Future Fellowship