Editing Maximal compact subgroup (section)

===Representation theory===
Maximal compact subgroups play a basic role in the [[representation theory]] when ''G'' is not compact. In that case a maximal compact subgroup ''K'' is a [[compact Lie group]] (since a closed subgroup of a Lie group is a Lie group), for which the theory is easier.

The operations relating the representation theories of ''G'' and ''K'' are [[Restricted representation|restricting representations]] from ''G'' to ''K'', and [[induced representation|inducing representations]] from ''K'' to ''G'', and these are quite well understood; their theory includes that of [[Zonal spherical function|spherical function]]s.