On a Compact Generalization of Association Schemes
We introduce a notion of compact association schemes, which serves as a compact analogue of classical (finite) association schemes. Our definition is formulated in a way that closely parallels the finite case, naturally admits a Bose--Mesner algebra, and includes the compact strong continuous association schemes introduced by Voit [J. Aust. Math. (2019)] within the framework of hypergroups. This approach provides a new perspective that bridges the theory of association schemes with harmonic analysis on compact homogeneous spaces.
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