On simple modules of Hecke algebras of type D_n

This is a continuation of our previous work. We classify all the simple ℋ_q (D_n) - modules via an automorphism h defined on the set {λ | D̃^λ ≠ 0}. When f_n (q) ≠ 0, this yields a classification of all the simple ℋ_q (D_n)-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 ℋ_q,1 (B_n)-module D̃^λ remains irreducible on restriction to ℋ_q (D_n).