Subrepresentation
In representation theory in mathematics, a subrepresentation of a representation of a group G is a representation such that W is a vector subspace of V and.
A finite-dimensional representation always contains a nonzero subrepresentation that is irreducible, the fact seen by induction on dimension. This fact is generally false for infinite-dimensional representations.
If is a representation of G, then there is the trivial subrepresentation:
