Abstract.
We consider characters of association schemes. We define a kernel like subset for a character. It is a generalization of the kernel of a group character, but it need not be normal. We give a necessary and sufficient condition for it to be normal. Using this condition, we can read all normal closed subsets from the character table.
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Acknowledgments. The author would like to thank Dr. Mitsugu Hirasaka for valuable conversations about character theory of association schemes.
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Hanaki, A. Characters of Association Schemes and Normal Closed Subsets. Graphs and Combinatorics 19, 363–369 (2003). https://doi.org/10.1007/s00373-002-0512-x
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DOI: https://doi.org/10.1007/s00373-002-0512-x