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Subrepresentation

If${\displaystyle (\pi ,V)}$ is a representation of G, then there is the trivial subrepresentation:

${\displaystyle V^{G}=\{v\in V\mid \pi ($g)v=v,\,g\in G\}.}

If${\displaystyle f:V\to W}$ is an equivariant map between two representations, then its kernel is a subrepresentation of ${\displaystyle V}$ and its image is a subrepresentation of ${\displaystyle W}$.

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.

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