Cyclotomic Hecke algebras: Jucys-Murphy elements, representations, classical limit

91 p.An inductive approach to the representation theory of cyclotomic Hecke algebras, inspired by Okounkov and Vershik, is developed. We study the common spectrum of the Jucys-Murphy elements using representations of the simplest affine Hecke algebra. Representations are constructed with the help of a new associative algebra whose underlying vector space is the tensor product of the cyclotomic Hecke algebra with the free associative algebra generated by standard m-tableaux. The classical limit of the whole approach, including the construction of representations, is given. The flatness of the deformation is proved without the use of the representation theory