What is Plancherel measure?

In mathematics, Plancherel measure is a measure defined on the set of irreducible unitary representations of a locally compact group G {\displaystyle G} , that describes how the regular representation breaks up into irreducible unitary representations. In some cases the term Plancherel measure is applied specifically in the context of the group G {\displaystyle G} being the finite symmetric group S n {\displaystyle S_{n}} – see below. It is named after the Swiss mathematician Michel Plancherel for his work in representation theory.