Subrepresentation

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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:

References[edit]

  • Fulton, William; Harris, Joe (1991). Representation theory. A first course. Graduate Texts in Mathematics, Readings in Mathematics. 129. New York: Springer-Verlag. doi:10.1007/978-1-4612-0979-9. ISBN 978-0-387-97495-8. MR 1153249. OCLC 246650103.