Two commuting operators associated with a tridiagonal pair (Q417584)

Let \(V\) be a finite-dimensional vector space over a field. The author considers an ordered pair of linear transformations \(A:V\to V\) and \(A^*:V\to V\) that satisfy certain conditions. The pair \((A, A^*)\) is called a tridiagonal pair. It is shown that there exist unique linear transformations \(\Delta :V\to V\), \(\Psi :V\to V\) that satisfy specific properties. Furthermore, these transformations are characterized by the fact that they commute.