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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: O. V. Ogievetsky and L. Poulain d’Andecy
Journal: Proc. Amer. Math. Soc. 142 (2014), 2929-2941
MSC (2010): Primary 20C05, 20F55
Published electronically: June 2, 2014
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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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Additional Information

O. V. Ogievetsky
Affiliation: Aix Marseille University, Center of Theoretical Physics, UMR 7332, Luminy, 13288 Marseille, France (On leave of absence from P. N. Lebedev Physical Institute, Leninsky Pr. 53,117924 Moscow, Russia)
Email: oleg@cpt.univ-mrs.fr

L. Poulain d’Andecy
Affiliation: Aix Marseille University, Center of Theoretical Physics, UMR 7332, Luminy, 13288 Marseille, France
Address at time of publication: Korteweg-de Vries Institute for Mathematics, University of Amsterdam, P. O. Box 94248, 1090 GE Amsterdam, The Netherlands
Email: lpoulain@cpt.univ-mrs.fr, L.B.PoulainDAndecy@uva.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11992-7
PII: S 0002-9939(2014)11992-7
Received by editor(s): May 10, 2012
Received by editor(s) in revised form: August 10, 2012
Published electronically: June 2, 2014
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2014 American Mathematical Society