Clifford theory for commutative association schemes

Clifford Theory for Association Schemes

Clifford theory of finite groups is generalized to association schemes. It shows a relation between irreducible complex characters of a scheme and a strongly normal closed subset of the scheme. The restriction of an irreducible character of a scheme to a strongly normal closed subset coniatns conjugate characters with same multiplicities. Moreover some strong relations are obtained.

Commutative association schemes

Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of inception, the concept has proved useful in the study of group actions, in algebraic graph theory, in algebraic coding theory, and in areas as far afield as knot theory and numerical integration. This branch of the theory, viewed in this collection of surveys a...

Classification of commutative association schemes with almost commutative Terwilliger algebras

We classify the commutative association schemes such that all nonprimary irreducible modules of their Terwilliger algebras are one-dimensional.

An Assmus-Mattson theorem for codes over commutative association schemes

Generalized Commutative Association Schemes, Hypergroups, and Positive Product Formulas

It is well known that finite commutative association schemes in the sense of the monograph of Bannai and Ito lead to finite commutative hypergroups with positive dual convolutions and even dual hypergroup structures. In this paper we present several discrete generalizations of association schemes which also lead to associated hypergroups. We show that discrete commutative hypergroups associated...