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A complete system of primitive pairwise orthogonal idempotents for theCoxeter groups of type $B$ and, more generally, for the complex reflectiongroups $G(m,1,n)$ is constructed by a sequence of evaluations of a rationalfunction in several variables with values in the group ring. The evaluationscorrespond to the eigenvalues of the two arrays of Jucys--Murphy elements.

Fusion procedure for Coxeter groups of type B and complex reflection groups G(m,1,n)