On a Compact Generalization of Association Schemes

Akifumi Nakada

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arXiv · 2511.02385

On a Compact Generalization of Association Schemes

Akifumi Nakada

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Abstract

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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Akifumi Nakada. 2026-03-13. On a Compact Generalization of Association Schemes. https://arxiv.org/abs/2511.02385

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