Geodesic
Central Idempotent Measures on Unitary Groups
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 719-725

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a locally compact group and M(G) the space of finite regular Borel measures on G. If μ and v are in M(G), their convolution is defined by Thus, if f is a continuous bounded function on G, μ is central if μ(Ex) = μ(xE) for all x ∈ G and all measurable sets E. μ is idempotent if μ * μ = μ.The idempotent measures for abelian groups have been classified by Cohen [1]. In this paper we will show that for a certain class of compact groups, containing the unitary groups, the central idempotents can be characterized. The method consists of showing that, in these cases, the central idempotents arise from idempotents on abelian groups and applying Cohen's result. 
Rider, Daniel. Central Idempotent Measures on Unitary Groups. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 719-725. doi: 10.4153/CJM-1970-082-5
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