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Plancherel measure : ウィキペディア英語版
Plancherel measure
In mathematics, Plancherel measure is a measure defined on the set of irreducible unitary representations of a locally compact group 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 being the finite symmetric group S_n – see below. It is named after the Swiss mathematician Michel Plancherel for his work in representation theory.
==Definition for finite groups==

Let G be a finite group, we denote the set of its irreducible representations by G^\wedge. The corresponding Plancherel measure over the set G^\wedge is defined by
:\mu(\pi) = \frac,
where \pi\in G^\wedge, and \mathrm\pi denotes the dimension of the irreducible representation \pi.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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