On Operator Fields in an Upper Triangular Toeplitz Form

Abstract

In this paper, we solve the problem of describing the coordinate transformations that preserve an upper triangular Toeplitz form of a given operator field. This problem is of fundamental importance in geometry, and its solution yields auxiliary transformations for the corresponding nondiagonalizable quasilinear systems. Surprisingly, this problem is closely related to the description of all Nijenhuis operators in the same form. This description, as well as the formulas for the aforementioned coordinate transformations, are given by the implicit formulas involving matrix-valued functions.