Group theory and generalizations Representation theory of groups Concept
Irreducible representation
Summary
An irreducible representation is a nonzero group representation with no proper nonzero invariant subspace. Irreducible representations are the building blocks of representation theory. For a finite group over the complex numbers, every finite-dimensional representation is a direct sum of irreducible ones, by Maschke's theorem.
Where this leads
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Further reading
About this page
| Tag | FX3NEFYFFN |
|---|---|
| URI | m2://FX3NEFYFFN |
| Kind | concept |
| Writing | W0 stub |
| MSC | 20C15 |
| Specializes | Group representation |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Brauer's height zero conjecture
- Representation theory of the symmetric group
- Schur orthogonality relations
- Monster group
- Character table
- Clifford theory
- McKay conjecture