On the number of irreducible modular representations of a PP and QQ polynomial scheme

Whereas results about the number of irreducible modular representations of finite groups are known, those of Bose–Mesner algebras of association schemes are not well understood. In this paper, we consider the number of irreducible modular representations of the adjacency algebra of some PP and QQ polynomial association schemes. These results should be helpful for investigating the structure of association schemes.