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  text: '# Advertisement\n\nRepresentation theory (which physicists and chemists sometimes just call [3g8]) is the study of how [3gd groups] $G$ act on [vector_space vector spaces] $V$. A central idea in mathematics is that, because [linear_algebra linear algebra] is so easy (compared to other parts of math), we should always try to extract linear algebra from any situation we can, and representation theory is a standard tool to apply when extracting linear algebra from a situation involving a [3t9]. \n\nIn physics, vector spaces appear naturally as [Hilbert_space Hilbert spaces] of [quantum_state quantum states] associated to physical systems, and representations of groups on these Hilbert spaces appear naturally as symmetries of the system. The study of these representations is a fundamental organizing principle of modern physics; for example, it is behind [Eugene_Wigner Wigner]'s [Wigner_classification classification of particle types]. ',
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