On the primitive idempotents of the Weyl group of type D_n

Let 4\text≤ n\in \bfN and W(D_n) the Weyl group of Type D_n ．Let K be a field and group algebra KW(D_n) is split semisimple on the field K．for each simple module U of KW(D_n ), we explicitly construct a quasi-idempotent z_U \in K\left W\left( D_n \right) \right (i.e., z_U^2=c_U z_U for some c_U \in K^ \times such that c_U^-1 z_U is a primitive idempotent and z_UK\left W\left( D_n \right) \right \cong U as a right KW(D_n )-module．The main results of this paper generalize the construction of primitive idempotents by Dipper and James on semi-simple group algebras of type A and B Weyl groups．