O. V. Ogievetsky, L. Poulain d`Andecy. On representations of complex reflection groups G(m,1,n)

Natural Sciences / Mathematics / Algebra

Submitted on: Sep 12, 2012, 17:34:16

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.