Reducibility of representations
A (unitary) representation
- irreducible iff
has no non-trivial -Invariant subspace. See Irrep - reducible iff
has at least one non-trivial -Invariant subspace, thus carrying a subrepresentation rep - completely reducible iff
can be written as the direct sum of irreps. rep
Properties
- A unitary representation is an irrep iff it is not the direct sum of nontrivial representations.
- Character irreducibility criterion