Equivariant spaces of matrices of constant corank one

Abstract

We classify all irreducible G$G$ ‐equivariant subspaces of Hom(V1,V2)$\operatorname{Hom}(V_1,V_2)$ of constant corank one, where G$G$ is a reductive group over an algebraically closed field of characteristic zero and Vi$V_i$ are irreducible representations. We give explicit necessary and sufficient conditions on the highest weights of the representations. This is the first general classification result of its kind, and it recovers, as a special case, some known examples arising from symmetric forms.