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arXiv · 1205.3459

On representations of complex reflection groups G(m,1,n)

O. V. Ogievetsky·L. Poulain d'Andecy
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Abstract

An inductive approach to the representation theory of the chain of the complex reflection groups G(m,1,n) is presented. We obtain the Jucys-Murphy elements of G(m,1,n) from the Jucys--Murphy elements of the cyclotomic Hecke algebra, and study their common spectrum using representations of a degenerate cyclotomic affine Hecke algebra. Representations of G(m,1,n) are constructed with the help of a new associative algebra whose underlying vector space is the tensor product of the group ring of G(m,1,n) with a free associative algebra generated by the standard m-tableaux.

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BibTeXRIS

O. V. Ogievetsky, L. Poulain d'Andecy. 2012-05-15. On representations of complex reflection groups G(m,1,n). https://doi.org/10.1007/s11232-013-0008-2

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