a representation D of G is reducible <=> D is equivalent to a direct sum of 2 smaller dimensional representations of G.

there exists M s.t. Forall g in G, D(g) = M^*
|D1(g) 0|*M

|0 D2(g)|

If a representation D is not reducible, it is called irreducible.

This is actually the definition of completely reducible but it is equivalent for all compact and finite groups.

source

jl@crush.caltech.edu index

irreducible

character

tensor