Explicit gauge fixing for degenerate multiplets: A generic setup for topological orders

We supply basic tools for the study of the topological order of a multiplet which is an eigenspace of a finite-dimensional normal operator with continuous parameters. We allow intrinsic degeneracies within the multiplet where a well-known standard procedure does not work. As an important example, we give novel expressions for a spin Hall conductance for unitary superconductors with equal spin pairing. Generic topological orders will be treated in this unified manner particularly with nontrivial topological degeneracies.