Bruhat Order for Two Flags and a Line

The classical Bruhat order describes the degeneration of a pair of flags from a more general to a less general relative position. The covers in this order (the minimal degenerations) correspond to reflections in the Weyl group. In this talk, we will describe the analogous situation for a pair of flags and a line. We classify the (finitely many) relative positions using quivers, and describe the covers, which involve cycles of length greater than 2. (Joint work with with J.Weyman and A.Zelevinsky.)