Geodesic
Actions of finite hypergroups.
Journal of Algebraic Combinatorics, Tome 18 (2003) no. 2, pp. 135-151.

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Summary: This paper is concerned with actions of finite hypergroups on sets. After introducing the definitions in the first section, we use the notion of $lsquo$maximal actions $rsquo$ to characterise those hypergroups which arise from association schemes, introduce the natural sub-class of *-actions of a hypergroup and introduce a geometric condition for the existence of *-actions of a Hermitian hypergroup. Following an insightful suggestion of Eiichi Bannai we obtain an example of the surprising phenomenon of a 3-element hypergroup with infinitely many pairwise inequivalent irreducible *-actions.
Keywords: hypergroups, actions, *-actions, association schemes 
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     title = {Actions of finite hypergroups.},
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Sunder, V.S.; Wildberger, N. J. Actions of finite hypergroups.. Journal of Algebraic Combinatorics, Tome 18 (2003) no. 2, pp. 135-151. http://geodesic.mathdoc.fr/item/JAC_2003__18_2_a0/