# unitary representation

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 $H$.

Title unitary representation UnitaryRepresentation 2013-03-22 16:51:45 2013-03-22 16:51:45 Mathprof (13753) Mathprof (13753) 4 Mathprof (13753) Definition msc 20C35 IrreducibleUnitaryRepresentationsOfCompactGroupsAreFiniteDimensional