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unitary representation (Definition)

Let $G$ be a topological group. A unitary representation of $G$ is a pair $(\pi, H)$ where $H$ is a Hilbert space and $\pi: G \to U(H)$ is a homomorphism such that the mapping of $G \times H \to H$ that sends $(g,v)$ to $\pi(g)v$ is continuous. Here $U(H)$ denotes the set of unitary operators of $H$ The group $G$ is said to act unitarily on $H$ or sometimes, $G$ is said to act by unitary representation on $H$




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See Also: irreducible unitary representations of compact groups are finite-dimensional

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Cross-references: group, unitary operators, continuous, mapping, homomorphism, Hilbert space, topological group
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This is version 1 of unitary representation, born on 2007-03-24.
Object id is 9111, canonical name is UnitaryRepresentation.
Accessed 1319 times total.

Classification:
AMS MSC20C35 (Group theory and generalizations :: Representation theory of groups :: Applications of group representations to physics)

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