Generalized quivers, orthogonal and symplectic representations, and Hitchin–Kobayashi correspondences

Abstract

We review the theory of quiver bundles over a Kähler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group [Formula: see text]. We first study the case when [Formula: see text] or [Formula: see text], interpreting them as orthogonal (respectively symplectic) bundle representations of the symmetric quivers introduced by Derksen–Weyman. We also study supermixed quivers, which simultaneously involve both orthogonal and symplectic symmetries. In particular, we completely characterize the polystable forms of such representations. Finally, we discuss Hitchin–Kobayashi correspondences for these objects.