Irreducible Representations of Wreath Products of Association Schemes
Akihide Hanaki
and Kaoru Hirotsuka
DOI: 10.1023/A:1025117409460
Abstract
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.
Pages: 47–52
Keywords: association scheme; irreducible representation; wreath product
Full Text: PDF
References
1. E. Bannai and T. Ito, Algebraic Combinatorics I: Association Schemes, Benjamin-Cummings, Menlo Park, CA, 1984.
2. Yu. A. Drozd and V.V. Kirichenko, Finite Dimensional Algebras, Springer-Verlag, Berlin/New York, 1994.
3. A. Hanaki, “Semisimplicity of adjacency algebras of association schemes,” Journal of Algebra 225 (2000), 124-129.
4. D.S. Passman, Permutation Groups, Benjamin, New York, 1968.
5. K. See and S.Y. Song, “Association schemes of small order,” Journal of Statistical Planning and Inference 73 (1998), 225-271.
6. P.-H. Zieschang, An Algebraic Approach to Association Schemes, Springer-Verlag, Berlin/New York, 1996.
2. Yu. A. Drozd and V.V. Kirichenko, Finite Dimensional Algebras, Springer-Verlag, Berlin/New York, 1994.
3. A. Hanaki, “Semisimplicity of adjacency algebras of association schemes,” Journal of Algebra 225 (2000), 124-129.
4. D.S. Passman, Permutation Groups, Benjamin, New York, 1968.
5. K. See and S.Y. Song, “Association schemes of small order,” Journal of Statistical Planning and Inference 73 (1998), 225-271.
6. P.-H. Zieschang, An Algebraic Approach to Association Schemes, Springer-Verlag, Berlin/New York, 1996.