Editing Peter–Weyl theorem (section)

===Representation theory of connected compact Lie groups===
The Peter–Weyl theorem—specifically the assertion that the characters form an orthonormal ''basis'' for the space of square-integrable class functions—plays a key role in the [[Compact group#Representation theory of a connected compact Lie group|classification]] of the irreducible representations of a connected compact Lie group.<ref>{{harvnb|Hall|2015}} Section 12.5</ref> The argument also depends on the [[Maximal torus#Weyl integral formula|Weyl integral formula]] (for class functions) and the [[Weyl character formula]].

An outline of the argument may be found [[Compact group#An outline of the proof|here]].