Definition

Subrepresentation and Invariant Subspace

Lie Groups and Lie Algebras · lie-groups.tex

Given a $G$-representation $(V, \rho)$ (Definition~Group Representation), a subspace $W \subseteq V$ is $G$-invariant (a subrepresentation) if $\rho(g)w \in W$ for all $g \in G$, $w \in W$. The restriction $\rho|_W$ then defines a representation of $G$ on $W$.

Depends on

Representation

Used in

Irreducible Representation
Irreducible Representation
Complete Reducibility

Dependency Graph

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