Solutions of the braid equation attached to power series

Let K be an algebraically closed characteristic 0 field and let V be the K-vector space with basis (Formula presented.). In this paper we use the theory developed in [17] to associate with each power series (Formula presented.) satisfying (Formula presented.), an involutive solution (Formula presented.), of the braid equation, and we begin the study of this correspondence. For (Formula presented.), let V_n be the subspace of V generated by (Formula presented.). Each one of the solution s(f) induces by restriction a solution (Formula presented.) on (Formula presented.). We also begin the study of these solutions.