Branes in the moduli space of framed sheaves

In the physicist's language, a brane in a hyperkähler manifold is a submanifold which is either complex or lagrangian with respect to three Kähler structures of the ambient manifold. By considering the fixed loci of certain involutions, we describe branes in Nakajima quiver varieties of all possible types. We then focus on the moduli space of framed torsion free sheaves on the projective plane, showing how the involutions considered act on sheaves, and proving the existence of branes in some cases.