Linked from

The 30 pages that link to Representation theory, each with the reason it gives.

• Gauge theoryRelated: Matter fields transform in representations of the gauge group.

• Group theoryRelated: Representations turn group operations into matrices that can be analyzed.

• Lie groupRelated: Representations turn Lie group symmetries into linear actions on vector spaces.

• Élie CartanRelated: Cartan’s work on Lie groups and algebras shaped the representation theory used throughout mathematics and physics.

• SymmetryRelated: It translates symmetry groups into matrices that can act on physical states and equations.

• Arthur CayleyRelated: Cayley’s permutation representation of groups anticipates a central way of studying abstract groups.

• Eugene WignerRelated: Its representations classify how quantum states transform under symmetry groups.

• Hermann WeylRelated: Weyl used representations to classify symmetries and organize quantum states.

• IsomorphismRelated: Representations translate abstract structures into concrete ones, often compared up to isomorphism.

• Harmonic analysisRelated: Group representations generalize frequency components to symmetries and structured spaces.

• Invariant theoryNarrower topic: Linear representations turn group actions into matrices acting on polynomial spaces.

• Emil ArtinRelated: Artin’s work connected group representations with L-functions and arithmetic.

• Richard BrauerNarrower topic: Brauer’s research made representations a central tool for studying finite groups.

• Abelian categoryRelated: Representations of a fixed algebra often form an abelian category suited to homological techniques.

• Erlangen programRelated: It develops group actions into a powerful language for connecting symmetry with algebra and geometry.

• Geometric group theoryCompared with: It studies group actions too, but emphasizes linear algebra rather than coarse space geometry.

• Jordan decompositionNarrower topic: Representations turn group and algebra elements into operators to which the decomposition applies.

• Noncommutative algebraRelated: Representations translate abstract multiplication into operators that can be analyzed.

• SU(2)Related: SU(2)'s irreducible representations classify angular-momentum multiplets and spin states.

• Pontryagin dualityRelated: Characters are one-dimensional representations, linking this duality to representation theory.

• Jordan–Chevalley decompositionNarrower topic: The decomposition helps analyze operators arising from representations of groups and algebras.

• Peter–Weyl theoremNarrower topic: The theorem is a landmark result linking representations to function spaces.

• Robert LanglandsNarrower topic: It supplies the language for translating arithmetic symmetries into linear algebra.

• Symmetry in quantum mechanicsNarrower topic: It is the broader mathematical discipline behind symmetry-based state classification.

• Ado's theoremNarrower topic: Ado's theorem is an existence result at the foundation of this field.

• Ngô Bảo ChâuNarrower topic: Representations provide one side of the correspondences that motivate the lemma.

• Wedderburn–Artin theoremNarrower topic: Semisimple ring decompositions reduce representations to simple components.

• Algebraic combinatoricsNarrower topic: It provides a central toolkit for translating combinatorial symmetry into linear algebra.

• Capelli identityNarrower topic: The identity supplies operator relations useful in studying representations of general linear groups.

• Mathematical formulation of the Standard ModelRelated: Representations assign gauge charges to matter and force fields.