Subrepresentation
In representation theory, a subrepresentation of a representation of a group G is a representation such that W is a vector subspace of V and .
A nonzero 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:
If is an equivariant map between two representations, then its kernel is a subrepresentation of and its image is a subrepresentation of .
References
[edit]- Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. Vol. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.