A family of tridiagonal pairs
Let \(V\) be a vector space of finite dimension over a field, and let \(A, A^*\) be a tridiagonal pair on \(V\) of diameter at least 3, whose eigenvalue and dual eigenvalue sequences, not all having multiplicity one, satisfy certain conditions. Given \(V = Mv^* + M^*v\), where \(M\) and \(M^*\) are the subalgebras of End\((V)\) generated by \(A, A^*\), and \(v\) and \(v^*\) are some eigenvectors of \(A, A^*\) respectively, in this paper a nice basis for \(V\) is found and the action of \(A, A^*\) on this basis in terms of six parameters is described.
scientific article; zbMATH DE number 2116544
scientific article