Geodesic
The subconstituent algebra of an association scheme. II
Journal of Algebraic Combinatorics, Tome 2 (1993) no. 1, pp. 73-103.

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Summary: This is a continuation of an article from the previous issue. In this section, we determine the structure of a thin, irreducible module for the subconstituent algebra of a $P$- and $Q$- polynomial association scheme. Such a module is naturally associated with a Leonard system. The isomorphism class of the module is determined by this Leonard system, which in turn is determined by four parameters: the endpoint, the dual endpoint, the diameter, and an additional parameter $f$. If the module has sufficiently large dimension, the parameter $f$ takes one of a certain set of values indexed by a bounded integer parameter $e$.
Keywords: association scheme, $P$-polynomial, $Q$-poiynomial, distance-regular graph 
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Terwilliger, Paul. The subconstituent algebra of an association scheme. II. Journal of Algebraic Combinatorics, Tome 2 (1993) no. 1, pp. 73-103. http://geodesic.mathdoc.fr/item/JAC_1993__2_1_a0/