Geometry and Topology

Equivariance in flag bundles and real structures

Equivariant vector bundles on flag varieties associated to a parabolic subgroup are well known to correspond to representations of the parabolic, and these in turn are related to quiver representations with relations. We discuss how to adapt these results in the presence of a real structure. In particular, we show that it is possible to reduce to the quasi split case, and that therefore one can still naturally relate to quiver representations. Time allowing, we will comment on the non-quasi-splt case, as well as the quiver bundle case.