Unitary representation

Summary

A unitary representation of a topological group $G$ is a homomorphism from $G$ to the unitary operators on a Hilbert space. It must be continuous in the strong operator topology. It is the kind of group representation used for infinite groups in analysis and physics, because unitary operators preserve lengths and angles. Harmonic analysis on a locally compact group is largely the study of its unitary representations. In quantum mechanics, symmetry groups act on state spaces in this way.