Geodesic
Two inequalities for parameters of a cellular algebra
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 82-95 
S. A. Evdokimov; I. N. Ponomarenko. Two inequalities for parameters of a cellular algebra. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part II, Tome 240 (1997), pp. 82-95. http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a6/
@article{ZNSL_1997_240_a6,
     author = {S. A. Evdokimov and I. N. Ponomarenko},
     title = {Two inequalities for parameters of a cellular algebra},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--95},
     year = {1997},
     volume = {240},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_240_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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