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Article Dans Une Revue Theoretical and Mathematical Physics Année : 2013

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

Résumé

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.

Dates et versions

hal-00961356 , version 1 (19-03-2014)

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O. V. Ogievetsky, L. Poulain d'Andecy. On representations of complex reflection groups G(m,1,n). Theoretical and Mathematical Physics, 2013, 174 (1), pp.95-108. ⟨10.1007/s11232-013-0008-2⟩. ⟨hal-00961356⟩
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