We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in arXiv: 1903. 06411. One case, however, namely the case of left-symmetric algebra b₁, ⏐, proved to be difficult. Here we solve it and, thus, complete the solution of the linearization problem for Nijenhuis operators in dimension two. The problem turns out to be related to classical results on the linearization of vector fields and their monodromy mappings.
Andrey Yu. Konyaev (Fri,) studied this question.