Editing Unitary representation (section)

{{Short description|Concept in mathematics}}
In [[mathematics]], a '''unitary representation''' of a [[Group (mathematics)|group]] ''G'' is a [[linear representation]] π of ''G'' on a complex [[Hilbert space]] ''V'' such that π(''g'') is a [[unitary operator]] for every ''g'' ∈ ''G''. The general theory is well-developed in the case that ''G'' is a [[locally compact]] ([[Hausdorff space|Hausdorff]]) [[topological group]] and the representations are [[strongly continuous]].

The theory has been widely applied in [[quantum mechanics]] since the 1920s, particularly influenced by [[Hermann Weyl]]'s 1928 book ''[[Gruppentheorie und Quantenmechanik]]''. One of the pioneers in constructing a general theory of unitary representations, for any group ''G'' rather than just for particular groups useful in applications, was [[George Mackey]].