×

zbMATH — the first resource for mathematics

Irreducible representations of wreath products of association schemes. (English) Zbl 1021.05098
Summary: The wreath product of finite association schemes is a natural generalization of the notion of the wreath product of finite permutation groups. We determine all irreducible representations (the Jacobson radical) of a wreath product of two finite association schemes over an algebraically closed field in terms of the irreducible representations (Jacobson radicals) of the two factors involved.

MSC:
05E30 Association schemes, strongly regular graphs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin-Cummings, Menlo Park, CA, 1984. · Zbl 0555.05019
[2] Yu. A. Drozd and V.V. Kirichenko, Finite Dimensional Algebras, Springer-Verlag, Berlin/New York, 1994.
[3] Hanaki, A., Semisimplicity of adjacency algebras of association schemes, Journal of Algebra, 225, 124-129, (2000) · Zbl 0942.05066
[4] D.S. Passman, Permutation Groups, Benjamin, New York, 1968.
[5] See, K.; Song, S. Y., Association schemes of small order, Journal of Statistical Planning and Inference, 73, 225-271, (1998) · Zbl 0935.05098
[6] P.-H. Zieschang, An Algebraic Approach to Association Schemes, Springer-Verlag, Berlin/New York, 1996.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.