 |
Johan van de Leur is interested in Lie (super)algebras, Lie groups and integrable systems. He studies irreducible highest weight representations of affine Kac Moody algebras, especially realizations of such modules in terms of differential operators. The corresponding Loop group orbit of the highest weight vector gives rise to hierarchies of soliton equations. One finds in this way e.g. the famous KdV-hierarchy. The representation theory of these Lie algebras and the geometry of the group orbit give a lot of information on the differential equations of the hierarchy, on its solutions and corresponding Bäcklund transformations. |
|
Here is an animation |