## Ögmundur Eiríksson (14/03/2019)

Math Colloquium

### Speaker: Ögmundur Eiríksson, Max-Planck-Institute for Mathematics, Bonn

### Title: Orbits in varieties of quiver representations

Location: VR-II 258

Time: Thursday March 14 at 11.40 am

### Abstract:

We recall the basics of representations of quivers.

On one hand we consider categories of representations and the varieties of such representations on the other. These varieties have a natural action by products of general linear groups, and the orbits correspond to isomorphism classes in the category of representations.

Next we consider the adjoint action of parabolic subgroups of general linear groups on their nilradical.

There is a description by Brüstle-Hille-Ringel-Röhrle of the orbits of this group action via the standard-filtered modules over the Auslander algebra of a truncated polynomial ring. This is one of many examples where orbits correspond to isomorphism classes of standard filtered modules over a quasi-hereditary algebra.

Recent joint work with J.Sauter considers the action of parabolic subgroups of general linear groups on compatible closed subvarieties of representation varieties for quivers. We show a connection to standard filtered modules that generalises that of BHRR.