Fixed-point subspace of a group action
= Fixed-point subspace of a group action
{title2=$\operatorname{Fix}(H)=\{v:hv=v\ \forall h\in H\}$}
= Fixed-point subspaces of a group action
{synonym}
For a linear <group representation>, the common fixed vectors of a subgroup form an <invariant subspace> for any <equivariant map> restricted to it. Its dimension is central to symmetry-based branching theorems. It need not be invariant under the entire group; conjugate subgroups have conjugate fixed-point subspaces.