Linear degenerations of flag varieties

Despite the title of the seminar, "Nonlinear Algebra Seminar", we focus in this talk on linear degenerations of the flag variety, which does appear prominently not only in representation theory. The flag vaeriety could be defined by the vanishing of Plücker relations, while by considering the flag variety in terms of Linear Algebra, the notion of quivers and their representations, and, following this, quiver grassmannians are naturally. A linear degeneration of the flag variety is then a degeneration of the flag variety when considered as a quiver Grassmannian of type A.

In the talk we discuss an order along the degenerations, the flat (irreducible) degenerations, meet the Catalan numbers and translate our degenerations into degenerate Plücker relations. This provides a link to the tropical flag variety *and maybe an approach how to compute the latter in some future*. (*means "dreaming")