# Plancherel measure on set of irreducible representations of a finite group

From Groupprops

(Redirected from Plancherel measure)

## Definition

Suppose is a finite group. Let be the set of irreducible representations (up to equivalence) of over the field of complex numbers. The **Plancherel measure** on this set assigns to each element of the measure where is the degree of the representation.

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