Harder-Narasimhan Filtrations of Hyperquiver Representations

Source abstract

Hyperquiver representations are generalisations of quiver representations. They are directed hypergraphs with vector spaces assigned to vertices, and for every directed hyperedge, an assignment of a linear map from the tensor product of the source vector spaces to the tensor product of the target vector spaces. We study the moduli of hyperquiver representations, where we use affine GIT to describe the (in)stability of such objects under the action of a product of general linear groups. Our main result introduces the Harder-Narasimhan filtration of a hyperquiver representation. We also derive a formula for the weights of this unique filtration, which specialise to the Harder-Narasimhan slopes of a quiver representation.