Abstract
In this paper, we generalize the results of [4] by constructing an isomorphism of type B between the Hecke algebra H(WBn)(p,q) and the group algebra of WBn (Weyl group of type B). The isomorphism thus constructed is compatible with Hoefsmit's model of irreducible representations of these two algebras. Moreover, the restriction of this isomorphism to a subalgebra of H(WBn)(p,q), isomorphic to the Hecke algebra of type D, allows one to establish an analogous isomorphism between the Hecke algebra of type D and the group algebra of the Weyl group WDn.
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