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# unitary representation

*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 $H$.

Related:

IrreducibleUnitaryRepresentationsOfCompactGroupsAreFiniteDimensional

Type of Math Object:

Definition

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Reference

## Mathematics Subject Classification

20C35*no label found*

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