Representation Theory
Explore linear actions; characters and decomposition; construction and lie theory. Concepts and connections are available independently of video coverage.
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Irreducible representations
An irreducible representation has no nonzero proper invariant subspace.
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Intertwining operators
An intertwiner is a linear map commuting with the represented group actions.
Invariant subspaces
An invariant subspace is preserved by every transformation in a representation.
Characters
A finite-dimensional representation's character assigns the trace of each represented element.
Complete reducibility
A representation is completely reducible when it is a direct sum of irreducible representations.
Group representations
A group representation is a homomorphism into invertible linear transformations.
Knowledge connections
- Invariant subspaces · Related · Map context
- Intertwining operators · Related · Map context
- Invariant subspaces · Prerequisite · Map context