Definition

Irreducible Representation

Lie Groups and Lie Algebras · lie-groups.tex

A representation $(V, \rho)$ (Definition~Group Representation) is irreducible (or simple) if $V \neq 0$ and its only subrepresentations (Definition~Subrepresentation) are $\{0\}$ and $V$ itself.

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flowchart LR classDef current fill:#6366f1,color:#fff,stroke:#4f46e5 nca6bd350["Representation"] n45f1bf4d["Subrepresentation and Invariant Subspace"] nc8a0881e["Irreducible Representation"]:::current nce9df6b9["Schur's Lemma"] nf1efa483["Maschke's Theorem"] n36e5bd4f["Schur's Lemma"] na4ca6986["Complete Reducibility"] nca6bd350 --> nc8a0881e n45f1bf4d --> nc8a0881e nc8a0881e --> nce9df6b9 nc8a0881e --> nf1efa483 nc8a0881e --> n36e5bd4f nc8a0881e --> na4ca6986 click nca6bd350 "../objects/ca6bd350.html" "_self" click n45f1bf4d "../objects/45f1bf4d.html" "_self" click nce9df6b9 "../objects/ce9df6b9.html" "_self" click nf1efa483 "../objects/f1efa483.html" "_self" click n36e5bd4f "../objects/36e5bd4f.html" "_self" click na4ca6986 "../objects/a4ca6986.html" "_self"