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Let $G$ be a Lie group which is compact and connected. Write $T \hookrightarrow G$ for the maximal torus subgroup.
A weight on $G$ is an irreducible representation of the maximal torus subgroup $T \hookrightarrow G$.
For $\rho : G \to Aut(V)$ a representation of $G$, and for $\alpha : T \to Aut(\mathbb{C})$ a weight, the weight space of $\rho$ with respect to $\alpha$ is the subspace of $V$ which as a representation of $T$ is a direct sum of $\alpha$-s.
In other words, the weight space of a $G$-representation for a weight $\alpha$ is the corresponding eigenspace under the action of $T$.
For connected compact Lie groups the
Peter Woit, Topics in representation theory: Roots and weights (pdf)
Wikipedia, Weight (representation theory)
Last revised on March 29, 2014 at 09:02:28. See the history of this page for a list of all contributions to it.