O. V. Ogievetsky, L. Poulain d`Andecy. On representations of complex reflection groups G(m,1,n)
Submitted on: Sep 12, 2012, 17:34:16
Natural Sciences / Mathematics / Algebra
Description: 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.
The abstract of this article will be published in the September 2012 issue of "Intellectual Archive Bulletin", ISSN 1929-1329.
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