@article{b80c255afac141439158fbaaa22c123e,
title = "On association schemes with multiplicities 1 or 2",
abstract = "Inspired by the work of Amitsur [1] on finite groups whose irreducible characters all have degree (multiplicity) 1 or 2, in this paper we study association schemes whose irreducible characters all have multiplicity 1 or 2. We will first show that the general case can be reduced to commutative association schemes. Then for commutative association schemes with multiplicities 1 or 2, we prove that their Krein parameters are all rational integers. Using automorphism groups of association schemes, we obtain a characterization and classification of those commutative association schemes all valencies and multiplicities of which are 1 or 2 in terms of Cayley schemes.",
keywords = "Association schemes, Automorphism groups, Cayley schemes, Krein parameters, Multiplicities, Quotient schemes",
author = "Mikhail Muzychuk and Bangteng Xu",
note = "Funding Information: Part of this paper was done during the visit of the second author at Ben-Gurion University of the Negev, Israel, in October 2018. He appreciates the hospitality of the first author and the support of the Center of Advanced Studies in Mathematics at the Mathematics Department of Ben-Gurion University of the Negev . The first author acknowledges the support of the National Science Foundation of China (No. 11971189 ). Funding Information: Part of this paper was done during the visit of the second author at Ben-Gurion University of the Negev, Israel, in October 2018. He appreciates the hospitality of the first author and the support of the Center of Advanced Studies in Mathematics at the Mathematics Department of Ben-Gurion University of the Negev. The first author acknowledges the support of the National Science Foundation of China (No. 11971189). Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = nov,
day = "1",
doi = "10.1016/j.jalgebra.2021.06.004",
language = "English",
volume = "585",
pages = "89--116",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}