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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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Cross-references: group, unitary operators, continuous, mapping, homomorphism, Hilbert space, topological group
There are 9 references to this entry.

This is version 1 of unitary representation, born on 2007-03-24.
Object id is 9111, canonical name is UnitaryRepresentation.
Accessed 556 times total.

Classification:
AMS MSC: 20C35 (Group theory and generalizations :: Representation theory of groups :: Applications of group representations to physics)
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