On Characters of a Class of P-polynomial table algebras and applications

Abstract

In this paper, we study the characters of homogeneous monotonic P-polynomial table algebras with finite dimension d>=5. We then apply them to association schemes. To this end, we develop some methods using tridiagonal matrices and Z-transform. Moreover, we calculate the eigenvalues of a special tridiagonal matrix which is found through the first intersection matrix of P-polynomial table algebras.