Abstract

We construct explicit homomorphisms between the generic Hecke algebra Hn(q) of type A and the degenerate affine Hecke algebra DH(Sn) by means of a generic element Rqν(X,S) which satisfies the quadratic Hecke relation. For the specialization of DH(Sn) by means of the Jucys-Murphy's elements associated with the symmetric group Sn, we obtain explicit isomorphisms, after extension of the scalars to C(q), between Hn(q) and the group algebra of the symmetric group defined over C(q). Moreover, this isomorphism is compatible with the Hoefsmit's model of irreducible representations of Hn(q) and Sn.

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