Abstract.
In the present paper we investigate the relationship between the complex representations of an association scheme G and the complex representations of certain factor schemes of G. Our first result is that, similar to group representation theory, representations of factor schemes over normal closed subsets of G can be viewed as representations of G itself. We then give necessary and sufficient conditions for an irreducible character of G to be a character of a factor scheme of G. These characterizations involve the central primitive idempotents of the adjacency algebra of G and they are obtained with the help of the Frobenius reciprocity low which we prove for complex adjacency algebras.
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Received: February 27, 2001 Final version received: August 30, 2001
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Hanaki, A. Representations of Association Schemes and Their Factor Schemes. Graphs and Combinatorics 19, 195–201 (2003). https://doi.org/10.1007/s00373-002-0498-4
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DOI: https://doi.org/10.1007/s00373-002-0498-4