Representation theory of non-classical GL(n) subgroups

We use newly developed techniques from Hopf algebra theory to provide (formal) group characters for subgroups of $GL(n)$ fixing a tensor $T_\pi$ of Young symmetry type $\{\pi\}$. New character formulae, branching rules, and generalized Newell-Littlewood theorems follow. The groups $H_{\{13\}}(n)$, being non classical in general, which stabilize an antisymmetric tensor of degree 3 will serve as an example showing furthermore the development of modification rules.