Representation theory in exactly solvable systems (2019–2024)

Abstract:
This project will develop the representation theory of Lie and generalized Lie algebras related to exactly solvable models. It will address many significant open mathematical problems. This project will also exploit several innovative ideas on the structure of quadratic algebras, Casimir invariants, differential operator realizations, roots systems, characters and indecomposable representations. This will give fundamental mathematical insight and allow the construction of new exactly solvable models. This will have an impact on theoretical physics as exactly solvable models play a central role in our understanding of a plethora of physical phenomena. As Lie algebras have applications throughout science, many more outcomes are envisaged.
Grant type:
ARC Future Fellowships
Funded by:
Australian Research Council