Two inequalities for parameters of a cellular algebra

Abstract

Two inequalities are proved. The first is a generalization for cellular algebras of a well- known theorem about the coincidence of the degree and the multiplicity of an irreducible representation of a finite group in its regular representation. The second inequality that is proved for primitive cellular algebras gives an upper bound for the minimal subdegree of a primitive permutation group in terms of the degrees of its irreducible representations in the permutation representation.