Plancherel measure on set of irreducible representations of a finite group

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Definition

Suppose G is a finite group. Let \operatorname{Irr}(G) be the set of irreducible representations (up to equivalence) of G over the field \mathbb{C} of complex numbers. The Plancherel measure on this set assigns to each element of \operatorname{Irr}(G) the measure d^2/|G| where d is the degree of the representation.

The Plancherel measure is a probability measure in the sense that the total measure of the set is 1. This follows from the fact that sum of squares of degrees of irreducible representations equals group order.