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A nonzero representation with no proper nonzero invariant subspace.
Irreducibility depends on the base field and the category of representations being used.
wp-irreducible_representationnlab-irreducible_representationEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Irreducibility excludes proper nonzero invariant subspaces.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-irreducible_representationnlab-irreducible_representationEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Over standard semisimple settings, irreducible representations have characters that organize decomposition and distinguish irreducible isomorphism classes under the stated hypotheses.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
etingof-representation-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Stable elementary particle species are classified by irreducible unitary representations of spacetime symmetry together with internal quantum numbers.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-physics-elementary_particlepdg-rppwp-irreducible_representationnlab-irreducible_representation