On simple modules of Hecke algebras of type Dn

This is a continuation of our previous work. We classify all the simple (?)q(Dn)-modules via an automorphism h defined on the set {λ | (?)Dλ≠0}. When fn(q) ≠ 0, this yields a classification of all the simple (?)q(Dn)-modules for arbitrary n. In general (i.e., q arbitrary), if λ(1) = λ(2), we give a necessary and sufficient condition (in terms of some polynomials) to ensure that the irreducible (?)q,1( Bn)- module (?)λ remains irreducible on restriction (?)q(Dn).