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

Ogievetsky, O.; Poulain d’Andecy, L.

doi:10.1090/S0002-9939-2014-11992-7

Fusion procedure for Coxeter groups of type $B$ and complex reflection groups $G(m,1,n)$
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by O. V. Ogievetsky and L. Poulain d’Andecy PDF

Proc. Amer. Math. Soc. 142 (2014), 2929-2941 Request permission

Abstract:

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

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