An important example of a class function is the character of a group representation. Over the complex numbers, the set of characters of the irreducible representations of form a basis for the vector space of all –valued class functions, when is a compact Lie group.
Relation to the convolution algebra
Class functions are also known as central functions, because they correspond to functions in the convolution algebra that have the property for all (i.e., they commute with everything under the convolution operation). More precisely, the set of measurable complex valued class functions is equal to the set of central elements of the convolution algebra , for a locally compact group admitting a Haar measure.
|Date of creation||2013-03-22 12:18:06|
|Last modified on||2013-03-22 12:18:06|
|Last modified by||djao (24)|