Approaching degenerations in classical Lie types
Magdalena Boos (Bochum)
Abstract: The Borel subgroup B of a classical Lie group G acts on the nilpotent cone N of nilpotent complex matrices in Lie G via conjugation. If N is restricted to the subvariety of 2-nilpotent matrices, then the number of orbits is finite and we can describe a parametrization of the orbits by combinatorial objects. By making use of a translation to the symmetric representation theory of a finite-dimensional algebra with self-duality, we are able to approach their orbit closures. Phenomena which arise in the different classical types will be discussed. This is work in progress with M. Bender, G. Cerulli Irelli and F. Esposito.