Symmetries of Richardson-Gaudin equations

Project level: Honours, Masters, PhD

Richardson-Gaudin equations arise in both the study of integrable quantum systems, and polynomial solutions of second-order differential equations.  In the integrable systems setting, they have a close connection to the representation theory of certain infinite-dimensional Lie algebras. In the differential equation setting, the structure of the equations is invariant under Moebius transformations, and particular instances gives rise to symmetries. This project will investigate the consequences of these invariances and symmetries for the corresponding representation theory.