Dipartimento di Scienze di Base e Applicate per l'Ingegneria

 

Abstract:

One of the best known group actions on an affine variety is the conjugation action of GL_n(C) on the nilpotent cone N of complex nilpotent matrices of square size n. In particular interesting is the fact that there are only finitely many orbits which are parametrized by the Jordan canonical form, i.e. by partitions. We generalize this setting by looking at parabolic conjugation on certain subvarieties of N. It is not clear, if the number of orbits is still finite and what the orbits look like. In this talk, we will focus on representation-theoretic methods with which we can examine the actions. Furthermore, we discuss known results and future goals.