Theorem

Schur's Lemma

Lie Groups and Lie Algebras · lie-groups.tex

Let $(V, \rho)$ and $(W, \sigma)$ be irreducible $G$-representations (Definition~Irreducible Representation) over an algebraically closed field, and let $T : V \to W$ be an intertwiner (Definition~Morphism of Representations).

Either $T = 0$ or $T$ is an isomorphism.
If $V = W$, then $T = \lambda\, \mathrm{id}_V$ for some $\lambda \in k$.

Depends on

Irreducible Representation
Morphism of Representations

Used in

Remark
Character Table of $S_3$

Dependency Graph

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